Wigan assistant manager Graeme Jones is set to leave the club, according to The Mirror.
St Johnstone want Jones to replace Derek McInnes as manager at the Scottish Premier League club after McInnes moved to Bristol City earlier this week.
Jones has been linked with the Swansea job in the past but opted to stay at the DW Stadium.
However, the 41-year-old is understood to be keen on a move to St Johnstone after spending three years at the club as a striker up to 2002.
Jones's playing career also included spells at Doncaster, Southend, Boston, Bury and Clyde.
Jones was Martinez's assistant at Swansea in 2007 and rejoined the Spaniard at Wigan in 2009.
