Reports in Italy suggest the Toffees goal-poacher has agreed personal terms on a move to the Gunners, who would reportedly have to pay up to £75-million to take him from Merseyside.
Lukaku is in France playing for Belgium at Euro 2016 and scored two goals against Republic of Ireland last week.
Arsene Wenger is in the market for a new striker and recently missed out on Leicester City marksman Jamie Vardy, who has signed a new deal and turned down the offer Arsenal submitted to him prior to leaving for England duty.