The American was only a couple of hours into his posting at Le Havre, the club he had joined following a short spell in Norway, when one of the staff he had inherited from Thierry Goudet came up with a proposition. Initially, it sounded interesting. There was a player, who was away representing his country, Bradley's new colleagues felt would benefit from a move. But after witnessing him in action Bradley knew, without any shadow of a doubt, Les Ciel et Marine had a talent - and a very special one at that - on their hands.
"When I took over there in November 2015, Lys was on duty with the French under-20's," Bradley says, describing the cold winter day in Normandy when he arrived at the Stade Océane. "I was asked immediately about sending him out on loan but replied I wanted to work with him for a few weeks before making that decision. The next week, when he came back, I went straight to the sporting director and said I wanted to keep him. I thought he was our best striker. I saw Lys as a number nine."
Mousset has excelled in a central role, for the club where he first turned professional, AFC Bournemouth and most recently Sheffield United. But the 23-year-old, who enters Saturday's game at Tottenham Hotspur searching for his fourth goal in only 11 outings for Chris Wilder's side, was not always tasked with finding the back of the opposition net. Indeed, as Bradley's words reveal, he was frequently deployed as a winger before heading to England.
To understand Mousset's story, and the qualities which have endeared him to folk at Bramall Lane, one needs to start at the beginning. The moment when, after impressing for a junior team in the city's eastern suburbs, he enrolled on one of the most successful youth programmes in France.
"Lys came here when he was nine or 10," Michael Bunel, Le Havre's technical director of Le Havre's pre-academy, says. "He was very powerful even then, very fast and with a very hard shot. That was one of the things which first came to our attention. I think he played only one season for Havre Caucriauville before coming to us. Of course he was raw and not very technical then, But that is one of the things, his first touch, that we worked on."
Bunel, who worked closely with Bradley when the former Swansea City manager first recognised Mousset's potential, also explains the player's personality helped accelerate his development. Chris Wilder, who paid £10m to acquire Mousset's services following United's promotion from the Championship, also referenced his character as a reason why, despite struggling for opportunities on the south coast, he believed the youngster would thrive in Yorkshire.
"The way he is as a person was key," Bunel continues. "He was always laughing and always smiling, basically he was just happy to be here, to play and to train. Never aggressive. He needed technical work but he was always ready in his mind to do that. Really, that is a key element to his success. Lys just loved football and so he was always willing to listen and to work."
After scoring 14 times for Le Havre's reserves, Mousset made a steady but unspectacular start to his career at senior level before blossoming under Bradley. Scoring 14 times in 28 appearances captured the imagination of Bournemouth's scouts who, after fending off competition from United's opponents this weekend, lured him to Dorset in 2016. Although chances there did not prove forthcoming - largely, Wilder has alluded, because of the presence of Callum Wilson and Josh King - United's faith in his potential has been rewarded. And, as he reflects upon Mousset's progress, Bradley knows his hunch was correct too. The qualities which have enabled him to hit the ground running at United were already in evidence during the 2015/16 Ligue 2 campaign.
"He was capable of coming off defenders, drifting wide and running at them," Bradley, now head coach of MLS franchise Los Angeles FC, says. "Lys needed work but he was strong and explosive. Additionally, he could hit a really heavy ball with his right foot. The confidence we showed in Lys paid off, he appreciated the work we did with him and he improved every week. He played a huge part in a season where Le Havre only missed out on promotion to Ligue 1 by a single goal. I can recall one, against Nimes in the second half of the season, that was phenomenal."
Speaking following his equaliser at West Ham, which followed a match-winning goal against Arsenal, Wilder cited Mousset's "explosiveness" as one of the factors behind United's decision to lure him north. Although the protracted nature of his move meant he was eased rather than thrust into action, Mousset has become increasingly prominent in recent weeks. Having opened his account at Everton earlier this term, he has started two of United's last three matches; including the win over Burnley which sees them travel to London ranked sixth in the Premier League.
Despite being a menance for defenders, there is a softer side to Mousset's character as Bunel reveals. It could also explain why, combined with increased exposure, he is thriving in a United squad Wilder acknowledges is built on togetherness.
"Lys is a child of this city," Bunel insists. "In the sense that his team mates and coaches will have become like family. If you think about it, young players might even spend more time with their colleagues than they do their own families. So team mates become like brothers. Your team becomes a second family."
"We always try and make good people here as well," Bunel adds, noting Le Havre have also produced the likes of Paul Pogba, Benjamin Mendy and Dimitri Payet. "I think the fact he went to England will have helped him grow as a person. He will speak the language and discovered a different culture. We are so pleased to see him doing well at United, very proud of him."
Bradley, who boasts spells in charge of the USA, Stabæk and Egypt on his managerial CV, graduated from Princeton University before becoming a coach. That cosmopolitan background means he also respects Mousset's willingness to build a life away from his hometown of Montivilliers. After leaving Le Havre to join Swansea City, Bradley admits he has another good reason for keeping an eye on United's results in the top-flight.
"It been great to see Lys development since going into the EPL," Bradley says. "Hopefully this will continue at Sheffield United. Additionally I had the chance to work with Oli McBurnie, who of course if also there now, at Swansea. I also saw his potentially and am glad to see him at Sheffield United also."