The Red Devils are rumoured to be preparing a £50m bid for the Croatian playmaker, who has been an integral figure in Spurs's title charge this season.
Tottenham appear to be stubborn in their attempts to retain the player's services, however, after rejecting numerous bids from Chelsea last summer.
United boss Sir Alex Ferguson is thought to be a long-term admirer of Modric and sees him as the answer to his side's central midfield problems.
Several injuries in that position have lead Paul Scholes to coming out of retirement, but the United legend is expected to hang up his boots again at the end of the season.
This would leave the Premier League champions short again, with Modric apparently top of Ferguson's wanted list.