Klinsmann and Pellegrini are reportedly out of the running for the Southampton job, leaving Puel as the new favourite.
Reports suggest Southampton are not in for Jurgen Klinsmann
The German had previously emerged as the bookies' favourite to over the helm at St Mary's this summer, overtaking former Manchester City boss Manuel Pellegrini as the most likely candidate to replace Ronald Koeman.
Southampton are looking for a replacement for Ronald Koeman after his move to Everton
But Klinsmann is understood not to be on the club's radar at the present time, with the Daily Echo even going so far as to claim he was not even on the shortlist of possible candidates.
Manuel Pellegrini is also reportedly out of the running for the Southampton job
Meanwhile, despite being heavily linked to the Saints hot seat since Koeman's departure, the club has reportedly decided against turning to Pellegrini, believing him to not be an ideal fit to take over the reins.
The club is still reportedly keen on bringing a new manager in before July 4th, with executive director Les Reed leading the boardroom effort in thoroughly assessing each candidate.
Claude Puel is now understood to the be the favourite for the job
Frenchman Claude Puel is now thought to be the front-runner for the job, while Vitor Pereira has also been linked, despite recently committing himself to Fenerbahce.