The Senegalese ace recently confessed that he is considering his future at Upton Park, suggesting that if a big club playing European football came in for him he would find it hard to pass up the opportunity.
And with his Toffees side on the verge of Europa League qualification, Roberto Martinez is thought to be keen.
The Spaniard currently has on-loan Manchester City man Gareth Barry running his midfield, yet there are lingering doubts as to whether or not he will stay beyond his season-long spell at Goodison Park.
Martinez wants the former England international – who will be a free agent in a few months’ time – to stay, however he is putting plans in place in case he cannot tie up an arrangement.
Diame is seen as a viable option, with his £3.5m release clause particularly attractive.
He may even go for less than that sum as his current contract is due to enter its final year when the season ends.