The Serie A side wanted to sign the experienced goalkeeper, but he was not interested in the move.
Former Manchester United goalkeeper David de Gea has rejected a move to Inter Milan this summer.
According to reports, the Spaniard is keen to make a return to La Liga, where United signed him while at Atletico Madrid. He grew up through the ranks of Atletico Madrid and played for them for two seasons before he switched to the Premier League.
Inter had offered a deal worth around £83,000 a week to De Gea, but the goalkeeper was not keen on it and preferred not to continue with talks with the Italian club.
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The coach's comments come as K'Ogalo stare at a possible ban from engaging in continental football.
Meanwhile, after De Gea's exit, United moved fast and signed his replacement, Andre Onana, a 27-year-old Cameroonian international.
"Walking out at Old Trafford to defend our goal and contribute to the team will be another amazing experience. This is the start of a new journey for me, with new teammates, and new ambitions to fight for," a hopeful Onana said after sealing the deal with Inter Milan to become a Red Devil.
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The striker, who scored 32 goals last season, has been linked with a move away from Tottenham after failing to win titles in England.
"Manchester United has a long history of incredible goalkeepers. I am excited by the opportunity to work again with Erik ten Hag, and I can’t wait to play my part in the success I know he is determined to deliver at this great football club."