Chris Wilder continues to keep faith with the 26-year-old by selecting the midfielder for his starting XI. Lundstram himself failed to rule out staying at Bramall Lane.
Speaking last week, the Liverpudlian said: "It's the same situation, everything's still on the table. We'll see what happens.
"Of course, [speculation] is bound to happen but I'm here and while I am here I'm committed, as you've seen in my performances.
"I'm 110 per cent and no-one can question that. Who knows what will happen but while I'm here, I'll give everything."
But given contract negotiations have been ongoing since last season, it does seem all-but certain he’ll leave United, four years after joining from Oxford United.
Where will he go? That’s the question on pundits’ lips, including former Scotland defender Alan Hutton, who name-dropped Leeds United.
“Is he going to go to a top-ten team? I’m not sure, it’s a difficult one,” he told Football Insider.
“Sitting here, I don’t really think there’s any team that I could go: ‘He’s definitely going to go there.’ Leeds United, somewhere like that, where he can get up pitch and attack, they like to flood forward, would he suit someone like that?
“I’m pretty positive that there’ll be a few teams keeping a close eye on his situation anyway, that’s for sure.”
It was reported by the same publication that Lundstram had turned down interest from Rangers, and Paul Robinson, England’s former number one, has a warning for him.
“Lundstram needs to be playing at a high level week in, week out if he wants to get a big move at the end of the season,” he said.
“It is difficult when you run your contract down if you have not got something sorted out. A lot of players in his position will already know the club they are joining next season, speaking from experience and to other players.
“If he is still trying to impress clubs at this stage he is running the risk of losing form, being dropped from the team or suffering an injury. That is always a big risk to take.
“I am surprised that the Rangers one has not materialised, I thought it was going to come to fruition. He would be a great signing for Rangers given the way Steven plays.
“Lundstram needs to play things very carefully.”
Here’s a round-up of the latest gossip doing the rounds across the Premier League:
1. City eye striker
Manchester City will prioritise signing a striker this summer, regardless of whether they lure Barcelona star Lionel Messi to the Etihad Stadium. Borussia Dortmund’s Erling Haaland remains Pep Guardiola’s main target. (Goal)
Photo: THOMAS KIENZLE
2. Spurs monitor Damsgaard
Tottenham Hotspur are monitoring Sampdoria midfielder Mikkel Damsgaard with his value tripling from the £5.2million the Serie A club paid to sign him last summer. (La Gazzetta dello Sport via Football Italia)
Photo: Alessandro Sabattini
3. Solomon confirms PL interest
Arsenal-linked forward Manor Solomon has confirmed that a number of Premier League clubs have expressed an interest in signing him. He said: “My dream is to play in England and it also seems to be the most realistic option for me.” (Goal)
Photo: Denis Doyle
4. Musa move falls through
Former Leicester City flop and free agent Ahmed Musa’s move to West Bromwich Albion has collapsed. The Baggies already feel they have stronger players in his position. (Birmingham Live)
Photo: GIUSEPPE CACACE