The Malian midfielder has been without a club since the summer when he left Paris Saint Germain, but Sky Sports understands that Sissoko is currently in London holding talks with Palace.
Sissoko, who has just turned 29, spent the latter part of last season on loan at Fiorentina, and has been linked with moves across the world, from Europe to the Middle East.
But a move back to England, where he was a big success with Liverpool and enjoyed three years before joining Juventus for £10million in 2008, is now on the cards.
Tony Pulis tried to sign Sissoko during his time with Stoke City, but is now hoping he can persuade him to bolster his relegation battle at Palace.
Written by Steve Milne