The 29-year-old has been a key player for the Magpies since arriving from Aston Villa in the summer of 2016, helping them to top-flight promotion back in 2017 after making 34 Championship appearances.
The Eagles are open to a loan move, and could also be willing to snap up the £5 million-rated Newcastle star on a permanent basis.
The Sun claims it will now be down to Magpies’ boss Steve Bruce to decide if he can afford to let Clark go, and it will be interesting to see what his decision is.
The versatile defender, who can also play as a left-back, featured in 13 games for Newcastle last term, with eight coming in the league after Fabian Schär, Jamaal Lascelles and Paul Dummett established themselves in Rafa Benitez’s pecking order ahead of him, and he could be open to leaving if he fancies his chances of regular football at Palace.
Bruce needs depth at the back, but could let Clark leave if Hodgson’s side are willing to meet the Toons’ asking price and Paris Saint-Germain’s Stanley N’Soki – who also plays at left-back and centre-back – arrives.