Speculation about the right-back has ramped up in recent months, with Manchester United strongly linked with a summer move for England international.
The fact Clyne is out of contract next summer has fuelled talk and Saints manager Ronald Koeman has repeatedly underlined the importance of knowing whether he would sign a new and improved deal or not.
Executive director Les Reed planned to sit down with the full-back after Saturday's defeat to Leicester and it appears there is a chance he could yet stay on the south coast.
Previous talks over extending Clyne's contract have stalled, but Press Association Sport understands negotiations over a new deal have reopened.
Whether a deal can be struck is another matter, but the resumption of talks is a positive move given it appeared all but certain the 24-year-old would be heading for the exit.
Clyne has been at Southampton since 2012 and has become a senior England international since making the move from Crystal Palace.
Source : PA