Former Burnley player Ade Akinbiyi, Rodriguez's mentor at Turf Moor, admits the 22-year-old is unlikely to stay with the Clarets.
"It doesn't look like Burnley will be able to keep hold of him," Akinbiyi said. "A lot of clubs are interested and you can understand why. Jay is a decent player and can play at the top level.
"He has a year left to go on his contract but I'm sure they will look at all the different offers and see where it goes from then."