The Toffees manager is in the final year of his Everton contract, and the report claims he’s waiting to see if the club can hold on to the likes of Marouane Fellaini and Leighton Baines before putting pen to paper on a new contract.
But Chelsea are thought to be ready to try and convince Moyes to join Chelsea should the Everton manager delay his decision any longer.
Roman Abramovich appointed Benitez as interim boss after Roberto Di Matteo was relieved of his duties at Stamford Bridge earlier this season, and while Abramovich is content with Benitez for the time being, there is a feeling that the Chelsea owner will look to bring in another name come the end of the season.
Benitez appeared to rule Chelsea out of the title race this week, after they dropped points at home again to Southampton.
And the former-Liverpool manager was not the most popular choice to replace the Champions League-winning Di Matteo, and Benitez has been under pressure ever since he joined the club. The animosity towards Benitez among the Chelsea fans has led the board to consider alternatives, although privately the Chelsea owner is thought to be very pleased with the Spaniard.
Abramovich could turn to Moyes then – a manager the Chelsea hierarchy are believed to have been impressed by. The Scot has worked wonders with the Toffees on a tight budget, and the Blues may look to lure him to Stamford Bridge with the offer of Champions League football and a bumper transfer budget.