De Gea has been a free agent since coming off contract at United a year ago.
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He has held talks with Genoa and Fiorentina, but personal terms have been deemed too rich by both Serie A clubs.
Instead, says Marca, the best chance for De Gea to find a club willing to meet his contract demands is with the Saudi Pro League.
Al Shabab and one unnamed rival are currently in contact with De Gea and his minders.