The 23-year-old has fallen out of favour under Tony Pulis at The Hawthorns and is free to start talking to other clubs in January as he enters the final months of his contract.
A number of teams are understood to be interested in the England international hopeful, who will almost certainly reject any offer of a new deal and could be available for as little as £300,000 if he moves abroad.
Albion would prefer to sell Berahino to a Premier League rival, meaning that they will receive a bigger compensation fee owing to his age, with Everton said to be leading the way.
The Daily Mail reports that the Toffees, who are also close to finalising a move for Charlton Athletic youngster Ademola Lookman, have opened talks with the Baggies over a potential transfer, although Newcastle United, West Ham United and Stoke City may also enter the race for his signature.
Berahino has not played for West Brom since September 10 and was recently sent to a conditioning camp in France to help him lose weight and build up his fitness.