Southampton will take on Claudio Ranieri's Fulham after the international break.
Sam Allardyce has been tipped to replace Mark Hughes at Premier League side Southampton.
Jardim is said to be high on Southampton's wishlist.
Southampton were on the wrong end of a thrashing when they travelled to the Etihad Stadium on Sunday.
Mark Hughes is under huge pressure in the Premier League but will Southampton really return to Gordon Strachan?
Mark Hughes could pay the price for Southampton's dismal Premier League start with former Monaco boss Jardim in the frame.
Southampton were battered 6-1 away at Manchester City on Sunday and have won just one of 11 Premier League games this season under Mark Hughes.
The pressure on Mark Hughes increased as Southampton were humiliated by Premier League champions Manchester City on Sunday.
Southampton and Newcastle United played out a goalless draw at St Mary's on Saturday.
The Saints winger feels his relationship with Mark Hughes has improved greatly thanks to a summer of change.