The giant Ivorian striker spent the latter half of last season on loan at Goodison Park from Monaco, who sent him away to gain experience straight after snatching his signature from Anzhi Makhachkala in a £14m deal.
He managed just one appearance in an injury hit spell on Merseyside, but rumours have suggested that Everton chief Roberto Martinez is ready to ask the Ligue 1 heavyweights if he can keep the 6ft. 8” goal-getter for another campaign.
But now Spurs are also in the fight, and are willing to cough up £2m to get Traore in for the 2014/15 campaign.
As well as Everton, Hull and West Ham are also keen, yet none of the trio are likely to offer such a figure for one season, which could see Tottenham win the race.
The Londoners are desperate to push ahead with transfer plans despite being without a manager, with chairman Daniel Levy willing to sanction move for top stars over the coming weeks.