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 拢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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