The England under-21 international has scored 12 goals for club and country this season, with speculation claiming Arsenal and Chelsea were monitoring his progress.
He stands to earn a significant pay rise on his current £850-a-week deal, as West Brom look to end the transfer rumours linking him with Arsenal and Chelsea once and for all.
Negotiations between West Brom and Berahino's agent have been ongoing for several weeks, but the report claims there's been a breakthrough and an announcement can be expected in the next few days.
The 20-year-old would have been free to discuss terms with Arsenal and Chelsea from January, as his current West Brom contract expires at the end of the season.
Baggies boss Steve Clarke admitted he could be tempted to leave if the club didn't move fast to tie him up to a new deal.
Goals against Manchester United and Arsenal brought him into the national spotlight, but the youngster has had his minutes managed by Clarke in recent weeks.