The 23-year-old stopper is yet to play a Premier League game for the side he joined in the summer, but injury to Butland and concerns over the fitness of Shay Given means the Dane is in line to face the Swans.
Haugaard, who joined from FC Midtjylland, played for The Potters in FA Cup matches against Doncaster Rovers and Crystal Palace earlier in the season.
Butland has been an ever-present for Stoke in the league this season and has been one of their leading lights. However, a fractured ankle picked up for England against Germany means he will miss the remainder of the season and the European Championships.
Given could become Stoke's oldest ever league debutant if he is selected ahead of Haugaard. Though the Irishman has only been back in first-team training for ten days after a long lay-off with a knee injury.
Butland's op goes well
The Stoke number one tweeted this morning that his operation had been a success.
As Butland deals with the heartache of missing out on tournament football for his country, he has backed his young understudy to succeed at The Britannia Stadium.
He told the Stoke City matchday programme that he will advise the young 'keeper to "just be calm and play with a smile on his [Haugaard] face".
He said while he understood that Haugaard has had to be patient in waiting for a starting berth in the Premier League, he believed it would be a "real opportunity" for Haugaard "to show people what he [Haugaard] is all about".
Mark Hughes and the Stoke fans will now be hoping that Haugaard, who impressed in pre-season, can help Stoke secure another top 10 league finish as their injuries mount.