The 19 year old is rated at £15m by the Toffees but he is said to be keen on a return to London after finding first team opportunities hard to come by under Everton manager Ronald Koeman this season.
Lookman moved to Goodison Park from Charlton Athletic last January and went on to make eight first team appearances under Koeman last term. £140m worth of investment over the summer means that the winger has moved down the pecking order.
The Gunners were interested in the teenager before his switch to Everton, and they are are reportedly on good terms with the player’s representative.
Much will likely depend on whether the Toffees opt to start Lookman between now and the next transfer window. So far this campaign, the England Under 20 World Cup star has not featured in the league whatsoever, with all four appearances coming in cup competitions.