Saints are looking for another striker and explored a swoop to bring in Joel Piroe from Swansea City before he joined Leeds United.
They have now been linked with Aberdeen’s Bojan Miovski, but he is not the Championship side’s main target.
The man that Southampton want above all others is Sunderland hitman Stewart.
Saints boss Martin is a big admirer of Stewart and is keen to take him to the south coast before the transfer window closes.
Stewart has yet to play for the Black Cats this season due to injury, but he is working his way back.
The striker could play in a behind closed doors match during September’s international break, but whether he will still be at Sunderland then is unclear.
Stewart, 27, has entered the final year of his contract at the Stadium of Light.
