The Premier League club are to launch a formal planning process for the scheme which would see an extra 11,500 seats added to the stadium.
The local council backs the plans, which will cost an estimated £15m.
But chairman Huw Jenkins said Swansea will only proceed with the plans after achieving a third successive season in the top flight.
The redevelopment involves adding extra seats on three sides of the ground, which is owned by the council and run by a three-way company involving the Swans, the local authority and the Ospreys regional rugby side.
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