The 31-year-old has spent the past seven years at the club, but his deal is due to expire in the summer.
The Mirrorsays Leeds are willing to offer the defender a renewal in the coming weeks.
Berardi has not played regularly this term, starting only four games this term. Only two of those starts have come in the Championship.
It is possible he will leave on a free transfer to a club that offers him more playing time.
However, Berard is very popular at the club among fans and his fellow players.