The British tabloid has also reported that Merseyside outfit Everton have an interest in the Brazil international, who joined Turkish giants Fenerbahce in the summer of 2014 on a free transfer.
Diego is one of the biggest names in the world football and played a role in Atletico Madrid’s success last season.
The 30-year-old Brazil international re-joined the Spanish club in January of last year and helped them win La Liga and reach the final of the Champions League.
However, Diego, who also won the Europa League with Atletico in 2012, has struggled in the Turkish Super Lig.
The Sun now reports that the former Werder Bremen and Juventus attacker could come “on the market at a low fee” at the end of the season.
Supremely talented and gifted with vision, Diego has not always been consistent, and at 30 he is arguably past his best.
However, the Brazilian would be a good fit - theoretically at least - to Everton’s style of football and is a player who could enhance Roberto Martinez’s midfield.
Villa, though, would be a different proposition. The Villans are currently struggling for survival in the Premier League, and if they go down to the Championship, then they are not going to be attractive to Diego, who has played Champions League and Europa League football in his career.