The Baggies rejected an offer from Tottenham Hotspur for the England Under-21 striker this month and the London club are preparing an improved bid, according to media reports.
Berahino, 22, scored 20 goals in all competitions last season and Pulis said the speculation was having a negative affect on his player's state of mind.
"It's very unsettling for him," Pulis told the BBC. "He's a young lad and he's a lovely lad who I've never had a minute's problem from.
"For other things to be happening around him it's very difficult for him. I just think the transfer window should close.
"It just takes everything away from what we're here for and that's the football. So close the transfer window and let the season start and then everyone can concentrate on the season."
Berahino started West Brom's first two matches but they sit bottom of the Premier League table with one point from three games.
West Brom chairman Jeremy Peace has said the club have no interest in selling Berahino and that he remains central to their plans.
(Reporting by Tom Hayward, editing by Ed Osmond)
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