United have come back with a new offer of €50 million, along with the possibility of an additional €5 million in add-ons.
The player in question is a 27-year-old Cameroon international who previously played under United manager Erik ten Hag at Ajax.
The club has already reached an agreement on personal terms with the player.
Last season, the goalkeeper had an impressive performance for Inter, making 41 appearances across all competitions, including the Champions League final where they were defeated by Manchester City.
Meanwhile, Inter is looking to secure replacements for the goalkeeper position and has set their sights on Bayern Munich’s Yann Sommer and Shakhtar Donetsk’s Anatolji Trubin.
United have been in the market for a new goalkeeper all summer, with David de Gea out of contract and leaving Old Trafford after 12 years of service.