Lookman, 20, joined the Bundesliga side on loan in January in what head coach Ralf Rangnick described as a "last-second" deal.
The England youth international repaid the patience with five league goals and Leipzig is now eager to tie him down on a permanent basis.
It seems set to face a fight for his signature with Marco Silva urging Everton not to budge, but Rangnick is keeping calm over the tug-of-war.
"We'll see. Let's just wait another week," the Leipzig boss said.
"When you turn back the time to the last day of the last transfer market, at 2:00pm we didn't even think about a loan of Ademola Lookman. It seemed impossible to get him.
"But four hours later we got the deal done. I said then that it wasn't a last-minute deal but a last-second deal.
"We don't plan to repeat this, because it was a very stressful situation for us. We'll just wait. When Everton wants to keep the player they will tell us. If not we'll see if there's a chance of still getting him."
Lookman is yet to feature for Everton in the Premier League this term.