Lookman spent the second half of last season on loan with the Bundesliga outfit, making 11 appearances and contributing five goals, including scoring a late winner on his debut against Borussia Monchengladbach after coming on as a substitute.
The 20-year-old was a product of Charlton Athletic's youth system and enjoyed two impressive years as part of their senior squad before making a £7.5 million ($9m) switch to Everton in 2017. He made 15 appearances for the Toffees in the first half of their last campaign but was sent to Germany by then-manager Sam Allardyce so that he could experience regular first-team football.
The England Under 21 international’s performances in a Leipzig shirt were encouraging enough for supporters to call for him to move to the club on a permanent deal, but it now seems more likely that he will remain on Merseyside to play under new Everton boss Marco Silva.
The German club have been told they would have to pay €33m (£30m/$38m) to secure the long-term signing of Lookman, which Rangnick has insisted just isn't possible at this moment in time .
"We keep our budget, a 30 million transfer is excluded," he told German publication Kicker.
"At the moment it actually looks like it's not working, but the emphasis is on 'at the moment’."
Leipzig finished sixth in the Bundesliga last season and failed to qualify for the Champions League, after finishing as runners-up the previous season. They also lost their talismanic midfielder Naby Keita to Liverpool this summer and Lookman would have been an ideal replacement going into their latest campaign.
Everton, in stark contrast, do not seem to have a starting XI spot available for Lookman after a very busy transfer window which has seen them bring in several new faces including Bernard, Andre-Gomes and Richarlison.
However, Silva is adamant that Lookman will remain with the club after returning for pre-season, saying: "Of course, Ademola is very much in our plans.
"He’s a good player. He did well on loan for five and six months and was happy there but now is our moment to make him happy here. He is a very good player. He is our present and our future.”