The Blackpool Gazette claims the Seasiders tabled an unsuccessful offer of £650,000 for Puncheon, although the club declined to comment when approached by Press Association Sport.
Tangerines boss Ian Holloway told the Gazette:
"I am definitely interested in signing Jason. He proved what he could do when he was on loan with us last season and I think he would add to our squad."
Holloway's Southampton counterpart Nigel Adkins would not be drawn on the player’s future.
"We have done a little MOT on him and assessed him from a fitness point of view, just to see where he is," he said.