The England under-21 international has been in spectacular form early this season, finding the net against Manchester United most recently in the club's 2-2 draw with Louis van Gaal's side.
As reported by the Daily Star, the £15m-rated forward is reject to turn down the chance to move to a top five club like United or Arsenal though, as he bids to stay at West Brom.
WBA boss Alan Irvine is increasingly confident that Berahino will stay at the Hawthorns amid interest from United, Spurs and Arsenal with regular first-team football a big draw.
"I think Saido has the maturity to realise if he keeps doing what he does he will make progress here and all sorts of things will open up at international and club level," Irvine said.
"If he keeps doing this, he will become a top striker and anything can happen." - Alan Irvine
The striker has been mentioned as a top target for Arsenal and United, with the Premier League giants ready to splash the cash again in the January transfer window after big summers.
Man United and Arsenal news
Both Arsenal and United spent big over the summer transfer window strengthening their squads, especially in attacking areas.
While Berahino is not needed by Manchester United, they have Robin van Persie, Radamel Falcao and Wayne Rooney already, Arsenal could definitely use a striker of Berahino's ability.
The 21-year-old forward is one of England's brightest attacking talents, and has displayed the kind of lethal finishing ability that Danny Welbeck has flashed on occasion this season too.
The duo would be a formidable partnership, and would excite Arsenal fans who already have a potent attacking midfield with Alexis Sanchez, Mesut Ozil and the rest.