The giant Ivorian forward joined the Toffees for the final months of the season from the Ligue 1 heavyweights shortly after they had snapped him up from AnzhI Makhachkala.
However injuries limited the 6ft. 8” goal-getter to just one outing.
Yet Roberto Martinez is keen to give him an extended chance, and is hopeful that Monaco will opt to allow him to stay on.
The Mediterranean side have recently made Dimitar Berbatov’s deal a permanent one and will welcome back Radamel Falcao from a lengthy injury lay-off ahead of next season.
As a result Martinez believes there is a chance that he will be allowed to remain on Merseyside to regain match fitness before returning to the Stade Louis II.
Traore himself is understood to be ready to stay put, with first-team opportunities after Romelu Lukaku leaves – which appears to be likely – set to be more freely available than at his parent club.
Although his physical presence is his outstanding characteristic, the 23-year-old is also known for his technical ability and deft touch.