The Mirror says Everton have a serious decision to make over Lookman with RB Leipzig set to offer £17million for the winger.
They've already seen two bids knocked back by the Toffees, who are keen to give the England under-21 star a chance this season.
Now, they're set to return with another offer, according to reports.
RB Peipzig coach Ralf Rangnick said: “I would imagine it is well known that we would like to see the player with us.
“It does not help us to give any developing reports. We have to see if it works."