The striker joined the 'Clarets' from Stoke last summer, but couldn't make his mark on the team last season after suffering from constant knee injuries which saw him make just three appearances in the league.
After such a difficult season, Sean Dyche is thought to be willing to let the forward go down to the Championship as he tries to get back to fitness after such a disappointing campaign last year.
The 'Lilywhites' began their Championship campaign with a 1-0 win over QPR on Saturday, and will hope that the former Ipswich striker will be able to help them improve upon a 7th place finish in the Championship last season, meaning they narrowly missed out on a place in the play-offs.
While Walters could be heading out of Turf Moor, it is expected that a few players will be coming in to the club in the coming days, after the capture of Ben Gibson was confirmed on Sunday and Swansea's Sam Clucas is also close to joining.