According to the Daily Mail, McCarthy - currently the head coach of Cape Town City - is interested in taking over the Buddies.
The former Porto striker, who won Europe's most prestigious club competition under Jose Mourinho in 2004, took over in Cape Town at the start of the 2017/18 season and steered his side to a fifth-place finish in the Premier Soccer League (PSL).
UEFA A-Licence coach McCarthy has lived in Edinburgh since retiring in 2013, having promised his wife that they would move there after his playing career was finished.
Another name reportedly on St Mirren's shortlist is Real Madrid legend Guti, who will be interviewed for the job according to Sky Sports.
The 41-year-old has been loosely linked with the Madrid top job vacated by Zinedine Zidane, while Spanish newspaper AS say he is also a favourite for the head coach role at Segunda Division side Alcorcon.
Guti, who made 542 appearances for Real Madrid as a player and won 15 trophies at the Bernabeu, currently coaches the Champions League holders' under-19s team.
St Mirren are searching far and wide for a new manager after Jack Ross left for Sunderland. Last season, the Paisley club lifted the Scottish Championship title after finishing 12 points clear of second-placed Livingston.
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