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The Spanish goalkeeper is searching for a new club after his Manchester United contract expired at the end of last month.
According to the Daily Record, Inter had offered a deal worth around £83,000 a week to De Gea, but the 32-year-old has ‘halted’ negotiations with last season’s Champions League finalists.
The report claims that De Gea’s preference is to join a club in the Spanish top flight, however, his options are limited.
De Gea came through Atletico Madrid’s academy and played two seasons in the first team with his boyhood club before joining United in 2011.
But a return to Atletico appears unlikely unless the club offload Jan Oblak this summer.
United, meanwhile, have completed their £47.2m (€55m) deal to sign Andre Onana from Inter.
The 27-year-old Cameroonian goalkeeper completed his medical at Carrington on Wednesday and travelled to the US on Thursday to join his new teammates for their pre-season tour.
‘To join Manchester United is an incredible honour and I have worked hard all my life to get to this moment, overcoming many obstacles along the way,’ Onana said.
‘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.
‘Manchester United has a long history of incredible goalkeepers, and I will now give everything to create my own legacy in the coming years.
‘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.’
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