According to Fotomac, Palace were chasing Tufan in the last transfer window with a potential deadline day deal falling through. Hodgson has continued to keep tabs on the Turkish international since then and was impressed with his performances last season in the Super Lig.
Tufan operates mainly as a holding midfield player but can also play as a right-back or on the right wing. His adaptability makes him an ideal candidate for Palace, who are looking for a midfield man but may also require cover out wide with both Wilfried Zaha and Andros Townsend linked with summer exits.
Tufan has six goals in 56 appearances for Fenerbahce since breaking into their first team in 2015 and could be available for as little as £2.5m. Palace face competition for his signature from Premier League rivals Fulham
The Eagles are thought to have leapt ahead of their competition with some reports even suggesting they have already lodged an initial bid for their man. Tufan is reportedly happy in Istanbul and currently harbours no ambitions to make a switch to the Premier League.
Fenerbahce may be forced to sell players this summer though to avoid Financial Fair Play sanctions, so his current club could play a part in convincing Tufan to make the switch to Selhurst Park.