The youngster has been constantly linked with the Clarets recently and he has been given a trial with the club with both the Old Firm clubs, Celtic and Rangers, interested in him.
Shankland became Ayr's youngest ever first team player last May when he made his debut against Brechin at the age of 15 years and 300 days.
He had a trial with Liverpool a year ago but he signed a two year deal with Ayr in the summer with chairman Lachlan Cameron saying: "Mark has a bright future and we believe moving to England or the Old Firm at this stage of his career would be the wrong move. We felt he'd progress more by staying at Ayr."
Should his trial prove successful and Burnley sign him then he would join the youth squad under Terry Pashley for the remainder of this season and next season. It would be a similar move to the one that brought Joe McKee to Burnley from Livingston in 2009.