The Mirror says Everton have rejected a second bid from RB Leipzig for Lookman.
Leipzig made an improved offer of £14m plus add ons.
But the Bundesliga side have seen their latest attempt to test the Toffees resolve to hang on to Lookman dismissed again.
The new bid for forward Lookman, 20, was an increase on Leipzig's opening bid of around £12m which was submitted last week.
But it will take an offer of at least £20m for Everton to consider letting Lookman leave.