The 24-year-old's future has been the subject of several fresh reports.
A first offer to take the midfielder on loan wasn't entertained by the north London side but their issue with the second is that it falls short of their valuation, the Mail claim.
At the same time, the Daily Mirror suggest Tottenham want to sign Marseille's Giannelli Imbula - with Stambouli offered as part of a swap deal. The report is more or less consistent with the Mail's.
Despite the Frenchman appearing popular with the Spurs faithful, then, it appears Pochettino and co have developed a lasting first impression of the 24-year-old.
Stambouli has been given very few chances during his first season at White Hart Lane and, should the club be as keen to sell as a number of sources are suggesting, it would seem enough has been seen of the midfielder to suggest he won't come on leaps and bounds in the future.
Stambouli was, however, given the rare opportunity of game time for Tottenham during the north London side's post-season friendly tour.