The Eagles have already shared transfer dealings with Newcastle this summer, bringing in winger Andros Townsend while forward Dwight Gayle has moved in the opposite direction in a separate deal.
Palace boss Alan Pardew is still seeking further additions as he looks to establish the club in the Premier League’s top half next season and Sissoko appears to be high on his list.
The France international is widely considered far too good for the Championship, and as such he seemingly has no plans on staying there as he looks to return to the top flight this summer.
Newcastle will naturally want to keep hold of a player they deem one of their best and their reported £35 million asking price reflects their intentions of scaring off potential suitors.
Palace have money to spend this summer, yet the report states how they deem the figure far to excessive for a player Pardew bought for as little as £1.5 million a few years ago.
Sissoko, 26, has made over 100 appearances in the Premier League and has been capped by France 44 times.