The player has previously attracted interest from English sides, with Nigel Clough's Burton Albion seeing a £200,000 offer for the player turned down during the summer.
Morgan has caught the eye of plenty of scouts in recent times following a series of fine performances.
The 20-year-old scored 10 goals last term, earning a call-up to the Scotland U21 side and already has six this season as his purple patch continues.
Morgan has just 12 months left on his contract and Swansea are hoping to seal a cut-price deal for the youngster in January.
Any move would be a huge loss for St Mirren, who are currently top of the Scottish Championship.