The Daily Star says United would reportedly be prepared to hand the Argentinian a lucrative contract to lure him to Old Trafford.
The 22-year-old has a host of admirers across Europe, with top clubs circling for the goalscorer.
And Sport says United and PSG are both trying to convince him to join them at present.
And the two club are said to have offered Martinez 'multi-million dollar contracts' as they look to win the race.
Barcelona are still in the mix as they have long maintained their own interest, and a move to the Nou Camp could be more appealing.