Manager Stale Solbakken has been impressed with the former Hearts centre-back’s performances this season, with Berra having missed just one league game so far.
The Norwegian obviously felt that the 27-year-old had to improve but has been delighted with the Scotland international’s response and is now willing to tie him down to new deal.
Berra’s current contract is set to expire at the end of the season and the Molineux outfit have opened negotiations over an extension.
Solbakken told the Shropshire Star: “We’re in talks with him, so we will see where it ends. Berra has been outstanding. He’s gradually getting better and better.
“He’s not Franz Beckenbauer, but he’s improved tremendously. I think he had a tendency to make excuses for everything, but he’s grown mentally.
“I think he had to sort out his head in terms of being tougher with himself.”
Southampton have announced plans for a two-week tour of China as part of their pre-season preparations for the 2018-19 season.