It has been reported that Saints are considering a move for the 25-year-old Swans captain, who has been a key figure for the Welsh club in recent seasons.
Last term he helped his side in reaching the Championship play-offs and scored in the semi-final second leg against Barnsley to fire Steve Cooper's side into the final.
Saints are not the only club to have been linked with Grimes. Newcastle United are also said to be interested in signing the Swansea captain.
But Southampton could hold an important trump card in any transfer talks by the way of young striker Michael Obafemi.
The 20-year-old forward has been linked with a move to Swansea on a number of occasions in recent months.