Lookman spent time on loan at the Bundesliga side during the second half of the last campaign, with five goals and three assists coming in 11 league appearances.
According to The Mirror, the form of the 20-year-old has resulted in Leipzig making a permanent offer in the region of £12m for the attacker.
However, the report claims that Everton have rejected the approach. with new boss Marco Silva planning on using the England Under-21 international in his first-team squad.
Lookman - who still has three years remaining on his Toffees contract - has made just four starts and 11 substitute outings in the Premier League since signing from Charlton Athletic in January 2017.