Chairman Huw Jenkins has previously spoken of his desire to add extra seating to the council-owned ground in order to meet demand for tickets for home games, providing the club are able to retain their Premier League status.
Swansea regularly sell-out games at their 20,500 capacity home and are eager to bring in extra revenue, with the club enjoying the greatest success of its 101-year history.
There are plans to increase the capacity of the stadium to a maximum of 32,000, with the club taking a piecemeal approach to the work.
The number of seats is set to rise to 22,000 during the summer, and they hope an additional 5,000 will be added in time for the start of the 2014-15 campaign.
But Jenkins is adamant the club will only press ahead with the expansion if it is deemed the right financial decision.
Jenkins said: "We will have a full planning application in for the end of March and once that is passed we will do part of the work towards the end of next season, starting with the East Stand. Once we get that moving we will go from there, but it all runs parallel to us still being in the Premier League and it being right for the club.
"If and when the final stage is complete, the capacity will be 32,000.
"The first part will take the figure to 22,000 this summer, and then it will be 27,000 with the first stage of development of the East Stand, which will start near the end of next season and run through the summer.
"We have to make sure we do it right but it will be led by how well we do on the field."