Newcastle United reportedly want six players sold this month.
The 25-year-old joined the club in January when Steve McClaren was manager but the Frenchman has not started any matches since Benitez took charge in March.
With that in mind, the defensive midfielder seems unlikely to play a big role for Newcastle this season and the Chronicle claims that the Spanish manager is willing to sell him.
The report goes on to claim that Benitez is hoping to offload at least five more fringe players on a permanent basis rather than loan moves.
The Chronicle claimed on the weekend that Saivet - who cost £4.5 million - has interested Ligue 1 side Saint-Etienne, though the French club are hoping for a loan.
Benitez will have wanted better for the pre-season favourites for promotion, but there is plenty of time to turn it around and the former Liverpool boss will be hoping that a win at home to Reading on Wednesday is the start of something special.