It is understood the Saints - who beat the Baggies in the Championship semi-final last season - have been impressed by Corberan for some time and are admirers of the Spaniard's methods.
It remains to be seen whether the Premier League strugglers formalise their interest in terms of an official approach after the axing of Russell Martin but for Albion it comes as yet more unsettling uncertainty around the head coach's role.
Corberan, in post for more than two years at The Hawthorns, is currently second favourite in the bookmakers' odds behind Sheffield Wednesday boss Danny Rohl. German Rohl was previously assistant to Ralph Hasenhuttl at St Mary's and has impressed since taking on the head coach role at Hillsborough. His Owls are currently ninth, one place behind Albion.
It is believed Southampton's hierarchy are supporters of Corberan's organised and solid defensive style and ability to keep clean sheets and deny opposition.
Last season's semi-final first leg at The Hawthorns, which ended 0-0 prior to the 3-1 second leg, was an example of that.
Working well amid financial restrictions - Albion had to reduce the wage bill significantly in the summer - is also an attractive quality to clubs, with the advantage of a higher calibre of attackers to work with.
Southampton's top-flight rivals Leicester City and Wolves have also held an interest in the Spaniard recently for similar reasons, but the Foxes were reluctant to pay compensation - Corberan would cost north of £3million, it is understood - and instead appointed Ruud van Nistelrooy. Wolves are poised to appoint Portuguese Vitor Pereira from Al Shabab in Saudi Arabia.
Albion boss' style is vastly different to that of sacked Saints boss Martin and Corberan's football is viewed as one that could help tighten up defences.
Corberan currently has issues to address at The Hawthorns with Albion having won just twice in 15 games, albeit Sunday's reverse at play-off chasing rivals Watford was just a first defeat in 13 games.
Albion are still eighth in the Championship and two points off the top six.