They have been warned nothing can be rubber-stamped until the fate of Leeds United and the 15 points is known.
The Western Mail report that the news was first revealed in e-mails sent to Swans fans by Patricia Brown, a customer services official for the league, which were posted on websites.
"At this stage it is not possible to confirm that Swansea City have been promoted from League One to the Championship," she was quoted as saying.
"In view of pending proceedings, we can only confirm the league table as it currently stands."