Marsch left Leeds United with the club 17th in the Premier LeagueSouthampton may well have ended their interest in making Jesse Marsch their new manager after talks broke down.
Negotiations have faltered over the length of any proposed contract, with American Marsch wanting longer than the short-term deal Saints wanted to offer.
First-team coach Ruben Selles will continue to take the team in training and for Saturday's match at Chelsea.
Southampton will continue looking for another replacement for Nathan Jones, who they sacked on Sunday.
However the club may also consider leaving Selles in charge for longer than they anticipated - and he may now have an opportunity to put himself in the running to be appointed as the club's new permanent manager.
Saints sacked Jones one day after a home defeat by 10-man Wolves left them bottom of the top flight, four points from safety.
Marsch was sacked as Leeds boss on 6 February after less than a year in charge of the Elland Road club.
The American took over at Leeds at the end of February last year with the club 16th in the Premier League and helped them avoid relegation to the Championship courtesy of a 2-1 win at Brentford on the final day of last season.
He has also been a manager at RB Leipzig, New York Red Bulls and Red Bull Salzburg.
Southampton's board have had interest from a number of other candidates, including former Everton boss Frank Lampard and DC United manager Wayne Rooney.
But they saw Marsch's style as being the best fit to galvanise the club's squad as they bid to avoid relegation.
The American was previously seen as a possible successor to Ralph Hasenhuttl, who was sacked in November.
