The Northern Ireland international sensationally rejected the chance to stay at Ibrox opting not to transfer his contract over to newco Rangers after captaining the club through four months of administration.
Charles Green’s Sevco company, which bought the assets of soon-to-be-liquidated Gers for £5.5million, are trying to retain the current playing staff but have had little success so far.
Davis could now be on his way to the newly promoted Saints after admitted that he needs to be playing at the highest level with Rangers facing demotion to the Scottish third division.
“Only those who know me will know how much Rangers mean to me.” he said.
“I signed a new contract last year, giving my best years to the club in the knowledge we’d be challenging for leagues and cups and in Europe year after year. That’s the reason I came to Rangers.
“My young family love life in Scotland but after all that’s gone on since administration in February there came a point when I needed to make a decision based on what was best for my short career.
“I am 27 and need to be playing at the highest possible level.”
St Mary’s boss Nigel Adkins is desperate to bolster his team after sealing a return to the Premier League seven years after they were relegated on the final day of the 2004/05 campaign.
The South Coast side have followed Norwich City’s path from League One to the top-flight with two promotions on the spin and Adkins will be able to sign Davis on a free transfer.
Rhys McCabe, Sone Aluko, Steven Whittaker and Steven Naismith have already opted to cancel their contracts followed by Allan McGregor, Kyle Lafferty and Jamie Ness on Wednesday.