The Sweden international has long been linked with a move to Old Trafford.
And with the transfer window around the corner, Jose Mourinho's side could be set to refresh their interest.
But the Mirror claim they'll face strong competition from Serie A side Roma, who also want to sign the 22-year-old.
They claim Benfica want £35m for Lindelof, with United valuing him about £10m less than that figure.
And apparently Roma are willing to pay £30m, which gives them the edge over Mourinho's side.
United have also been linked with a move for Burnley defender, and Red Devil youth product Michael Keane.
But they're not likely to land him on the cheap either, with Clarets chairman Mike Garlick saying he'll gladly turn down transfer fees if it means Burnley surviving in the Premier League for another season and letting him walk away for free when his contract runs out next summer.
“Let’s roll it forward a year, what’s the prize for staying up again? Another £120-130m?" he said.
“So if we miss out on one or two fees and get that, I know what I’d take.
“The most important thing for the fans to know is that we don’t actually have to sell any player.
“Going forward it’s got to be on our terms and terms that are right for us. Do we need to sell anyone? No. If we want to keep players, we’ll keep them.”
