West Brom are an established club in the Premier League, while Burnley got promoted back into the English top flight at the end of the 2015-16 season.
Cooper has been on the books of Leeds since the summer of 2014 when he joined from Chesterfield for a transfer fee reported by talkSPORT to be worth £600,000.
The 24-year-old plays primarily as a central defender, but he can also feature as a left-back.
During the 2014-15 campaign, the Scotsman scored one goal and created three chances in 29 Championship appearances for Leeds.
The defender had a pass accuracy of 72% and a shot accuracy of 43%, and won 91 headers, 11 dribbles and 40 tackles.
Cooper scored one goal and created 10 chances in 38 league games for the West Yorkshire outfit last season.
The former Hull City man had a pass accuracy of 73% and a shot accuracy of 17%, and won 132 headers, 16 dribbles and 36 tackles.
Leeds fans have taken to Twitter to give their reaction to speculation linking Cooper with West Brom and Burnley.
Below are some of the best comments:
Cooper to WBA? Erm, ok. Decent enough, but Prem quality? Hmmm #lufc— LUFCInc (@LUFCInc) July 5, 2016
Seeing people saying to accept bids for Cooper and Mowatt....when will we learn to keep good young players not ship them out!? #LUFC— Alex Metcalf (@AlexMetcalfLUFC) July 4, 2016
Cooper was our best CB last season. Nothing too flashy but pretty solid and consistent, should be first CB on the teamsheet. #LUFC— Alex Metcalf (@AlexMetcalfLUFC) July 4, 2016
I like Liam Cooper, decent pro who gives his all, but if any offer comes in over £3m I would take it personally. Keep the youngsters! #lufc— Steve Jennings (@steve_jennings) July 4, 2016
To be honest I wouldn't sell Cooper, every footballer makes mistakes like every other person #lufc— Harry Chapman (@Harry_chapman17) July 4, 2016
I'd actually hold on to Cooper....he would be a fine player with better beside him and behind him #lufc— Sean (@ROI_LUFC) July 4, 2016