Martin is well down the pecking order at St Mary's and Saints boss Mauricio Pochettino is thought to be open to letting him move on.
The 23-year-old joined Southampton from non-league Eastleigh in 2009 and he has made 22 appearances for the first-team.
Martin found himself out of favour at Southampton in 2012/13 and spent last term out on loan at Crystal Palace and Coventry City.
Coventry are keen to re-sign Martin after the defender impressed during his time at the Ricoh Arena - making 12 appearances for the Sky Blues.
However, any move is being held up by Coventry's transfer embargo, with Steven Pressley making Martin one of his top targets this summer.