The 20-year-old Northern Ireland international was the subject of a failed bid from Celtic last year and the Hoops have again been linked with the Clarets frontman.
"It may be that I might have to consider staying at Burnley or even moving to Scotland," he said. "I will leave it up to my club, but if an offer came in from Celtic and Burnley accepted it, I would give it due consideration."
Former Northern Ireland captain Neil Lennon quit international football after his move to Celtic provoked sectarian abuse, which reached a head when he was the subject of a death threat.
Lafferty said: "Obviously, I am aware of what happened to Neil Lennon from Northern Ireland when he joined Celtic from Leicester City. But I am also aware that those days are gone now, thankfully. I know my family will support me no matter what I do.
"I am only 20 and I still have three years left on my Burnley contract. By the age of 23, hopefully, I will be a better, stronger player, I'll have developed more and maybe that might be the time to consider my future."