The 20-year-old English winger is due to return to Merseyside in July, but Rangnick says he would be willing to discuss terms with the English Premier League club and the England Under-21 international after being impressed by what he has seen of him.
"If it were only up to us, then I would already know the answer," Rangnick told Kicker magazine when asked if he would like to keep Lookman. "But it's not only up to us – there's no option in his contract. We'll have to see what happens in the summer, and it also depends on what happens at Everton."
Watch: Lookman's second Bundesliga goal saves Leipzig in Bremen
Lookman has started only three games since arriving in Leipzig during the winter break, but he has scored crucial goals when springing from the bench. The super-sub netted the winner against Borussia Mönchengladbach on his debut, while he came on to salvage a precious point against Werder Bremen last weekend.
Lookman has three years left to run on his contract with the Toffees, although his opportunities in their first team were limited in the first half of the season, when he started only once and came on six times in the Premier League.
Leipzig may therefore be able to lure him back next season, with the prospect of regular Bundesliga football and potentially a place on the UEFA Champions League stage for the latest English talent to come of age in Germany.