Indeed, according to the Guardian, West Brom director Richard Garlick outlined details of a series of Tottenham bids for the young striker that were 'way off the mark' shortly after Deadline Day.
But what would have happened had Spurs got their man?
West Brom, for one, would be nowhere right now. But Tottenham would have had a big solution to their lack of depth up front.
As Opta stats show, no other West Brom player has scored more than two Premier League goals this term (and only one has scored more than once), while Berahino has netted three times in just 485 minutes.
Slowly, Berahino is repairing his bond with the Baggies faithful - and getting back into a goalscoring rhythm.
But look at Tottenham's lack of goals, too. No Spurs player has netted more than the 22-year-old so far this Premier League season, who would have provided the perfect cover for the out-of-sorts Harry Kane.
West Brom fans should be delighted, then, that the north London side couldn't land one of their primary targets. Without Berahino, Tony Pulis's men would be woefully short of goals.