The Potters have made a bid for the 27-year-old winger.
Lennon has fallen down the pecking order in north London, with Andros Townsend interestingly playing ahead of him in Tottenham's last couple of games.
Stoke's interest in the winger had previously been reported, as well as their desire to bring Mousa Dembele on board.
ESPN now report a new development, however, in that the Potters have made a bid for the 27-year-old.
Lennon is Tottenham's longest-serving player but speculation has been rife about his future, with this January seemingly the perfect opportunity for Spurs to offload him if they really want to do so.
The club want £7 million, according to the report, although Stoke face competition from the likes of West Ham, West Brom and Leicester City.
Tottenham beat Chelsea 5-3 yesterday in their biggest win of the Premier League season by far. Stoke, meanwhile, drew 1-1 with Manchester United at the Britannia Stadium.