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 his patience with five league goals and Leipzig are now eager to tie him down on a permanent basis.
They seem 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 told a media conference.
"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, after a summer of big changes at Goodison Park.
New manager Marco Silva has made an immediate impact by revamping the squad, signing a number of new players including Lucas Digne and Yerry Mina from Barcelona and Richarlison from fellow Premier League outfit Watford.
Silva addressed the speculation linking Lookman with a permanent switch to Germany in a press conference on Thursday, as he told reporters: “He is our player. You know what my technical opinion of the player is and the player knows. For me it is not an issue,”
With seven days left before the European transfer window slams shut in Germany this story could develop in the coming days, with the new domestic campaign in both countries already well underway.