The 6ft. 8” striker spent the latter half of last term at Goodison Park after signing for the Toffees immediately after completing a move to the Ligue 1 runners-up from Anzhi Makhachkala.
Much was expected from the 23-year-old, but a troublesome hamstring injury hindered his playing time and limited him to just the one goal.
But that has not deterred Everton from pushing to get him back, with Roberto Martinez convinced the Ivorian can help the club to cope without Romelu Lukaku – whose loan spell has also ended.
The Spaniard wants to bulk out his squad for the challenges of Europa League football, and is aware that a goalscorer is need.
Even though Monaco are yet to field their man, they may be tempted to let him spend some more time on Merseyside to recover from his fitness worries and progress with regular action.
Traore is known for his lanky frame, but has been praised for his reading of the game and technical ability.