Goal understands that the two clubs are close to an agreement over a loan move for the player, which will include a non-binding purchase clause.
Negredo turned down two offers from China earlier in the summer, but is keen to return to the Premier League after spending the 2013-14 campaign with Manchester City.
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Valencia, meanwhile, were hoping for a permanent deal, but the Teesiders favour a loan given Negredo's less than scintillating form over the last two seasons.
The Liga side, however, will benefit to the tune of €7 million in their Financial Fair Play budget, although a transfer worth just under €10m has not yet been ruled out.
If the forward completes the move he will work under fellow ex-Real Madrid man Aitor Karanka, who has pushed hard for his signing as Middlesbrough look to strengthen their squad for the first year back in the top flight.