The Saints are back on the top table of English football after earning promotion via the Championship playoffs at the end of the 2023-24 campaign.
The South Coast club were too strong for West Bromwich Albion in a semi-final clash before pitting their wits against Leeds United in the final at Wembley.
Joining Southampton during the summer of 2023 from fellow second-tier outfit Swansea City, Martin guided his side to promotion at the first time of asking.
Since making the switch from South Wales over a year ago, the 38-year-old has managed 61 competitive matches for the Saints, winning on 32 occasions.
Southampton eyeing up Graham as Martin replacement?
According to Football Insider, there are significant movements occuring in the background at Southampton as they prepare for a potential managerial switch.
The report claims that the Saints are lining up a swoop for Potter to become their next head coach should Martin leave the South Coast club.
It is understood that the club's hierarchy are unhappy with the team's start to the 2024-25 campaign, leaving their 38-year-old boss on thin ice.
Martin supposedly has Monday night's clash at Bournemouth to save his job, with the Saints still searching for their maiden win of the Premier League term.
Potter has been without managerial employment since leaving American-owned Chelsea in April 2023, managing just 31 games for the West Londoners.
Southampton's worrying start
Although tipped by many for serious struggles in the Premier League, Southampton have arguably started poorer than some expected this season.
Hurtling towards the October international break, the Saints are without a win from five top-flight contests, meaning that they sit 19th in the early standings.
There is a real question over whether Martin's expansive style of football can work in the Premier League given the quality of their opposition.