The 25-year-old Senegal international has impressed since moving to Upton Park last summer and is a player Hammers boss Slaven Bilic would be loath to lose.
Kouyate was a virtual ever-present last season, making 30 Premier League starts, and has continued his good run of form this term, netting in West Ham’s surprise win at Arsenal on the opening weekend of the campaign.
The Sun states that Tottenham are confident that the former Anderlecht man wants a move to White Hart Lane and such a switch would offer Mauricio Pochettino a fresh option in the centre of the park, with the West Ham man also capable of filling in as a centre-back if necessary.
Pochettino has cleared the decks with regards to his contingent of midfielders with Paulinho, Etienne Capoue, Benjamin Stambouli and Lewis Holtby having all been sold this summer.
Tottenham have started the season poorly, collecting three draws in their opening four Premier League fixtures and still without a win, and Pochettino may feel that deadline-day deals are necessary if his North London side are to challenge for a top four spot.