Beyer joined the Clarets on loan last summer and has been a big part of a Burnley side who have completely dominated the Championship this season.
The 22-year-old centre-back has been a constant in the Burnley defence when fit and is one of the trusted lieutenants of Vincent Kompany on the pitch.
And it has been claimed that Beyer is likely to continue at Burnley if they get promoted to the Premier League.
According to German daily the Rheinische Post, the two clubs worked out an option to buy in the loan agreement last summer.
The clause will be triggered if Burnley get promoted to the top flight of English football at the end of the season.
Burnley will have to pay a fee of €15m to Gladbach if they wish to buy Beyer on a permanent deal.
With Burnley 22 points clear at the top of the table, they are almost a certainty to get promoted this season.
And Kompany could be keen to then keep hold of Beyer.
