Lookman played under Saints manager Ralph Hasenhuttl while on loan at RB Leipzig last season.
The former Charlton youngster forced his move to the Bundesliga and is said to have enjoyed his spell under Hasenhuttl’s management.
Despite Lookman’s return of five goals in seven league starts when at Leipzig for the second half of the 2017/18 season, Lookman has struggled to get a look in at Everton under manager Marco Silva.
Lookman has only started one Premier League game under Silva, though he scored in Everton’s 2-1 win over Lincoln City in the FA Cup last weekend.
Leipzig were reportedly interested in completing the full signing of Lookman in the summer. But, according to Sky Sports, Everton were asking for a fee of around £28 million.
If Saints were to pay such a fee, that would smash the club’s record transfer fee paid.