According to journalist Duncan Castles, both clubs will go head-to-head over the Brazilian this summer.
"It's a player that Chelsea have been watching for quite a while actually, but they've made some enquiries as to his availability and what his financial demands would be to join them, and that's Thiago Mendes, the Lille midfielder who has been part of their extremely oppressive French championship season where they look set to finish second in the French league," he told The Transfer Window podcast.
"They recently beat Paris St-Germain 5-1 at home to stall Paris St-Germain's crowning as the French champions again. He is one of several players in the Lille squad who Lille are ready to sell this summer if they get good offers for.
"He's now a candidate for also Everton. They were considering him in January when it looked possible that Paris St-Germain might take Idrissa Gueye from them and they saw Thiago as a potential replacement for Gueye."