The north London side had bids for Berahino rejected up until and including Deadline Day, as reported by the Daily Telegraph among many others.
He said during a 'Tackle Keown' session on the Daily Mail website: "I think Tony Pulis very cleverly stepped aside from the transfer controversy so that he could easily step back in again. Jeremy Peace has taken the brunt of the criticism but Pulis has been able to stay out of it for the most part and that was a clever move.
"He has met with Berahino and his mother and I think he is the right kind of man to get Berahino back onside. Now it is all about the timing of bringing him back, that is what Pulis will be concerned with."
Should Berahino feature for West Brom this weekend, it will be very interesting indeed to judge the reception he gets at the Hawthorns - when the Midlands outfit host Southampton.
Tottenham, meanwhile, will be without the 22-year-old but supporters will still be expecting a greater return than during their opening four Premier League games of the season.
Harry Kane has returned from the international break off the back of two England goals, while boss Mauricio Pochettino may be able to turn to Heung-Min Son and Clinton Njie for refreshed options out wide.