The current capacity of the Liberty Stadium, which replaced the Vetch Field as Swansea's home in 2005, is 20,500 with Swansea submitting plans to the city's council for an increased capacity of 33,000.
They will be joined in the Premier League next season by arch-rivals Cardiff City, who won promotion back to the top flight on Tuesday after a 51-year absence.
In a statement on their website the club said: "The works proposed would see the extension of the North, South and East stands of the stadium in a phased manner over the next three to five years.
"The proposals seek to capitalise on the success of the football club during their first two seasons in the Premier League, help consolidate this status and remain part of the top flight for many years to come."
Liberty Stadium is currently the second smallest ground in the Premier League with only Queens Park Rangers' Loftus Road ground smaller at 18,500.
Swansea have enjoyed a successful first two seasons in the Premier League, finishing 11th last season and are currently ninth after winning their first major trophy, the League Cup, in February. earning them a place in next season's Europa League.
The club just announced a record £15.9 million net profit for the six months up to the end of November 2012.
- Sports & Recreation