The central midfielder was set to move back to the Premier League, but a move to Burnley never materialised.
Now he could get the chance to move to Stoke, with the Championship side offering Swansea £8 million according to The Sun.
It is unclear whether Clucas will consider the move. He may want to wait until January for a move to the Premier League.
His move to Burnley was scuppered in part due to an injury, which will keep him out for another month.
But Stoke are not concerned about his injury and are ready to get the deal done.