The Baggies striker will not have to report back for training until Monday, while the rest of his team-mates are due back on Friday.
It is understood the England Under-21 international is set to be disciplined and, although no official meeting is planned, he is likely to speak to head coach Tony Pulis at some point.
Albion rejected two deadline days bids from Tottenham on Tuesday for the England Under-21 forward before Berahino suggested he would down tools on Twitter.
His message read: “Sad how i cant say exactly how the club has treated me but i can officially say i will never play Jeremy Peace.”
Baggies chairman Peace, who also rejected Berahino’s transfer request, insisted he would not be sold after meeting with the 22-year-old last week while he also said in a statement on Tuesday the club must move on.
“I said selling Saido so late in the window was not on our agenda,” said Peace, who rejected four bids in total.
“Tottenham’s offers failed substantially to reflect Saido’s true value while the timing made no allowance for our own recruitment of a suitable replacement for a proven Premier League goalscorer.
“Saido has been unsettled to the point where our head coach has not felt able to select him for our last three games.
“We are now left with the task of repairing the damage created by this unfortunate episode.”
It is understood Tottenham’s Tuesday bids were only marginally better than the north London club’s second offer, made last month, which would have only risen to £21million with clauses and add-ons.
The Baggies are understood to be unhappy with Spurs’ approach to the deal, which only strengthened their resolve to keep Berahino.
Albion have had to deal with deadline day drama before as, in 2013, Peter Odemwingie was disciplined after the forward drove to Loftus Road on deadline day without permission only for a proposed move to QPR to collapse.
West Brom stated no fee had been agreed and he was not free to discuss personal terms with Rangers.
In March last year Nicolas Anelka was sacked for gross misconduct after he refused to apologise for a ’quenelle’ gesture when he celebrated a goal at West Ham in December 2013.