The Star understands Derby County were among those clubs to express an interest in the Cardiff City centre-forward ahead of his move to Bramall Lane on loan.
Millwall are also known to have made an approach for Madine, while officials in Wales were contacted by another side competing with United and County for a top six finish only to be informed South Yorkshire was the player's preferred option.
City manager Neil Warnock, Chris Wilder's predecessor at United, has also confirmed he wanted the 28-year-old to join his former employers.
Madine, previously of Sheffield Wednesday and Bolton Wanderers, is expected to make his debut for third-placed United against Queens Park Rangers this weekend.
Beating County to the striker's signature will have been a sweet moment for Wilder and his staff after their counterparts at Pride Park outbid them for Martyn Waghorn at the beginning of the season.
Despite acknowledging he is a controversial figure among United supporters, Madine's desire to help their push for Premier League football is known to have impressed both Wilder and senior members of his squad.
Captain Billy Sharp, once criticised by Madine on social media, personally backed the move while Wilder is believed to have spoken at length with Warnock about his contribution behind the scenes at the Cardiff City Stadium before following-up his initial enquiry.
Madine, who represented Wednesday between 2011 and 2015, helped City gain promotion to the top-flight last term after completing a Â£6m move from Greater Manchester. He has made six appearances, five of those coming in the Premier League, for the Welsh outfit this season.