Pochettino is preparing for his second season in charge at White Hart Lane, and he has already overseen a number of exits from the first team squad.
Younes Kaboul, Paulinho, Etienne Capoue and Benjamin Stambouli have all left the club, but more players are expected to leave in the coming weeks.
In a bid to accelerate the departures of Lennon and Adebayor, Pochettino has now sent the duo to train with the club's development squad, according to the Daily Mirror.
The report suggests that Everton - who took Lennon on loan in January - are keen to sign the winger permanently, but Tottenham's £9m valuation is causing problems.
A move to Goodison Park on a full-time basis would be ideal for Lennon, and the uncertain future of Toffees wide man Kevin Mirallas could help the 27-year-old make his return to Goodison Park.
Meanwhile, the report also states that Tottenham have been in talks with Aston Villa over a deal to send Adebayor to Villa Park, where he would reunite with his former Spurs boss Tim Sherwood.
Villa have just lost Christian Benteke to Liverpool, which could now cause Sherwood to ramp up his interest in Adebayor - which would free up funds for Pochettino to sign a new striker to help Harry Kane in the Spurs attack.