Lookman, who joined Everton last summer in a £10m deal, struggled to for game time under both Ronald Koeman and Sam Allardyce before he was sent out on loan to the Bundesliga in January.
The 20-year-old impressed whilst playing in the Bundesliga, registering five goals and three assists in his 11 appearances for Leipzig, who finished the season in sixth place, qualifying for next year's Europa League.
As per the report, Lookman's turn in form has caught the eye of both Spurs and Southampton, but the Premier League duo face stiff competition from the German club, who are keen for Lookman to return on a permanent deal and have already held talks with the Toffees.
The versatile midfielder is also thought to be open to remaining in Germany following his successful loan spell and failed to rule out a move to Leipzig after a 3-0 loss to Mainz back in April, revealing, via Bundesliga.com: "I've been asked this question so many times.
"My loan is until the end of the season and I'm focused until the end of the season. Whatever happens, happens. It's out of my control."
Former Toffees boss Sam Allardyce had previously claimed that the club would be open to offers for Lookman. Everton, however, are understood to be reluctant to let the youngster go now that Marco Silva has been appointed as their new boss.