Mauricio Pellegrino is expected to face the chop if he fails to lift Southampton out of the relegation zone in the next week.
Mark Hughes, who was sacked by Stoke earlier this month, has already been earmarked as the 46-year-old’s replacement.
The Saints side were given a timely boost as they cruised into the FA Cup fifth round on Saturday with a 1-0 win against Watford.
But the victory does not aid Pellegrino’s battle against relegation, and the board are demanding at least four points from the next two games.
Southampton will host Brighton on Wednesday, before a crucial relegation battle with West Brom on Saturday.
The Saints are slumped at 18th in the top flight table, with just 22 points from 24 outings.
The Saints boss admitted that he is on the ‘electric chair’ at Southampton as his drab run continues.
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Pellegrino was appointed first-team manager of the Saints last summer after Claude Puel was controversially dismissed.
But the Argentinian has endured a roller coaster ride at St Mary’s, with fans chanting for him to be on sacked on several occasions.
Hughes has emerged as a target for the relegation-threatened side after being axed by the Potters in January.
The clubs board are said to be faithful that his experience can help guide the struggling Saints to safety.
Ex-Watford boss Marco Silva was also linked to the position just days after being sacked.