The 22-year-old Morocco international, who played a key role in Montpellier's march to the Ligue 1 title last season, has already agreed terms with Fenerbahce, but with the two clubs struggling to agree a fee, Tottenham are believed to have entered the race for his signature.
Montpellier president Louis Nicollin is willing to let the playmaker leave during this month's transfer window, yet turned down an initial offer of £6m plus add-ons from the Istanbul club.
He is understood to want closer to £12m, although a bid of £10m is expected to suffice.
Nicollin said: "I will let him leave, and I think he wants to leave as well. If they rise to €15m, everything will go through."
Despite Fenerbahce's advanced talks, L'Equipe have reported that Tottenham have also begun negotiations with the player's representatives.
Their interest comes despite a drop in form from the heights of last year, when Montpellier rated Belhanda at €60m on their way to being crowned French champions.
They now appear keen to cash in on one of their prize assets, whose current contract expires at the end of next season.
Belhanda has made 22 appearances so far this season, scoring eight times, and is currently preparing to represent Morocco at the Africa Cup of Nations in South Africa.