The midfielder was linked with a move to Goodison Park earlier in the summer but the rumours have resurfaced this week after United completed the signing of Ander Herrera.
The Blues have reportedly been tracking the 24-year old since January and are looking to put together an £8m bid for the midfielder. With the signing of Herrera, Cleverley has fallen further down the pecking order at Old Trafford and may look to move for more game time.
He previously played under Martinez at Wigan and enjoyed his time with the Latics. He endured a miserable season last year, receiving widespread criticism from United and England fans alike for his performances.
However, reports suggest the Red Devils are looking for a fee in excess of £10m due to the players' age, which Everton are unlikely to pay.
Would you like to see Everton sign Tom Cleverley? Vote and comment below.