According to BBC Sport, Spurs had as many as four bids rejected for the 22-year-old striker, who himself expressed his anger at not getting the move he desired on social networking site Twitter on transfer deadline day.
Berahino was left out of the Baggies’ last three matches, but Tottenham’s summer transfer target is back in contention and could feature against Southampton at The Hawthorns in the Premier League on Saturday.
West Brom boss Pulis believes that North London outfit Tottenham will not make another bid for Berahino in the future.
"Personally I don't think Tottenham will ever come back," the Baggies manager told Sky Sports. "I don't think that will happen…
"I just think most probably the two clubs have tried to do a deal and it's not worked and not happened.
“I don't see Daniel (Levy, Tottenham chairman) coming back to try to sign Saido again. I might be wrong. It is not anything. It's just my feeling. I just don't see Daniel coming back.”
West Brom are 15th in the Premier League table at the moment with four points from as many games, while Spurs are a place and a point behind them.