According to talkSPORT, there is a divide within the club's leadership regarding the disappointing start to the season.
While some believe they do need to improve quickly, others are being more patient towards Martin.
Southampton slumped to a 3-1 defeat at bitter rivals Bournemouth on Monday night.
Martin is liked by sporting director Rasmus Ankersen, but the club’s Serbian billionaire owner Dragan Solak is not impressed with how the season is panning out so far.