The Argentina international saw an approach by United about a loan deal rejected by Villa earlier this summer.
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The Sun says now United are making a fresh attempt, knowing Martinez has already approved the move.
Their approach for Martinez has been made in parallel with talks for Royal Antwerp goalkeeper Senne Lammens.
A first offer from United has been rejected, though they're making a new offer this weekend.
There's been claims Lammens could be in Manchester today for a medical.