Stoke or West Ham would have to splash out around £5 million to get their hands on the player - who would join Chelsea-owned Michael Hector in earning a Premier League move from Reading.
Cooper, who impressed in a League Cup tie against Everton earlier this season, is a former England under-19 international who turns 21 next month.
The local lad has been in the Reading first-team picture since 2014 and only extended his contract at the Madejski Stadium in October until 2018.
Cooper has played ten times for Reading this season and scored his first goal of the season last time out against Sheffield Wednesday.
The talented defender would be a gamble for either Stoke or West Ham - as he has not yet proved his credentials in the Championship.
Reading will be looking to keep hold of Cooper as a potential replacement for Hector, who could finally switch to Chelsea in the summer.