The Saints sit 19th in the table with just one point from eight matches and 18 goals conceded which is the second most in the league with only Wolverhampton Wanderers, who sit bottom, having more.
Martin’s side have lost their last 3 games and after a collapse at Leicester City despite having a 2-0 lead at half time many have called for him to be sacked.
However, Sky Sports have reported that the club’s hierarchy want to avoid an emotional move which could hurt the long term plans set in place by Martin after promotion last season.
The report says that Saints are "keen to avoid hasty decision-making based on emotion, instead retaining emphasis on the club's long-term strategy".
Martin’s struggling side visit Premier League winners Manchester City on Saturday with the Daily Echo reporting that the board have low expectations of a shock result meaning the game will not affect his position as head coach.