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Russell Martin was axed by the Saints following their 5-0 mauling by Tottenham Hotspur on Sunday.
And Corberan, who has been linked to a number of jobs in the past year due to the work he has done at Albion, quickly emerged as a leading contender.
Initial reports suggested Sheffield Wednesday boss Danny Rohl, who previously served as assistant manager at St Mary's, was one of the front runners.
But it is understood no contact has been made between the two parties - and Sky Sports have reported that Southampton are still considering Corberan as one of their candidates.
In the latest reports, Corberan has been named alongside former Denmark boss Kasper Hjulmand, with ex-Roma boss Daniele de Rossi also being linked to the job.
The links to Southampton comes after it was revealed he had become a target for Wolves, prior to their sacking of Gary O'Neil.
It is understood that Corberan has a release clause worth more than £2m built into his contract, and it is unsure at this stage whether the Saints would be willing to pay it, to bring the Spaniard to the South Coast.
According to the bookmakers, it is very much a three horse race, with Rohl currently their favourite at 6/4.
With most bookmakers, Corberan is currently third favourite to leave Albion for Southampton, with most offering 13/2.