Berardi, 33, departed Leeds last summer following the end of his contract and left Elland Road as a firm fan favourite and hugely popular in the dressing room.
He has since been a free agent and it has been unclear whether the 33-year-old would hang up his boots.
However, according to Swiss outlet 442.ch, he is now training at top flight side Sion.
The 33-year-old defender is working on his fitness at Sion and it is suggested he could be signed on a free transfer by the club.
Sion sit in seventh spot in the ten-team Swiss top flight and have conceded 35 goals in their 18 league games so far this season.
Adding Berardi to the ranks would offer another defensive option and the former Leeds man could join as a free agent.
The Swiss league is currently on its winter break and Sion are not due to be back in action until the end of the month, when they play Grasshoppers.
Despite having been capped by Switzerland, Berardi has never played senior football in his native country.
