The Gunners have had several bids rejected by United, who insist the World Cup finalist is not for sale, despite her being in the final year of her contract.
Arsenal’s pursuit of Earps could be similar to their move for England team-mate Alessia Russo. United refused to sell the striker initially but she eventually joined on a free transfer this summer.
Earps is in demand after an impressive World Cup campaign in Australia, where she was a key part of Sarina Wiegman’s side who battled to the final before a heartbreaking 1-0 defeat by Spain in Sydney.
The 30-year-old played every minute for the Lionesses at the tournament, conceding just four times in seven matches, deservedly claiming the Golden Glove award for the tournament’s best goalkeeper.
Earps also fought to have her replica England ‘keeper shirt put on sale to fans, with manufacturers Nike eventually making a U-turn and pledging to sell the kit in limited quantities.