The 30-year-old penned a short-term contract with Brentford back in January and is now on the radar of several clubs after his remarkable return to the top level.
After being fitted with an implantable cardioverter defibrillator, Eriksen left Inter Milan and trained with Erik ten Hag's Ajax before heading back to the Premier League.
Eriksen took some time to build up his match fitness, but he ultimately made 11 appearances for Brentford in the top flight and produced one goal and four assists.
The Denmark international's efforts helped the Bees secure Premier League survival, and Thomas Frank is still holding out hope that he will extend his stay at Brentford.
"We hope he'll decide in two weeks - he'll call me and tell me what he wants to do," Frank told AS when questioned on Eriksen's future recently.
European-competing clubs are preparing to step up their interest in Eriksen, but according to The Guardian, the Dane has no interest in a move to Old Trafford.
The report claims that Eriksen is more likely to stay at Brentford than sign for Man United, and he could also still make a sensational return to Tottenham Hotspur two-and-a-half years after his departure.
Eriksen made 305 appearances for Tottenham between 2013 and 2020, registering 69 goals and 90 assists, and the Lilywhites are said to hold an interest in reuniting with the playmaker.
Eriksen also worked under Antonio Conte during his underwhelming period at Inter Milan, but Spurs are yet to formally follow up their interest.
The Brentford midfielder's rejection should see Man United ramp up their efforts to sign Barcelona midfielder Frenkie de Jong after losing no fewer than four midfielders on free transfers.
CEO Richard Arnold has confirmed that the Red Devils are hoping to strike a deal for the 25-year-old, but Barcelona are holding out for an €85m (£73m) fee and have already turned down a £60.1m proposal from Man United.