Spurs have had two bids rejected for the Albion striker, who saw a transfer request dismissed by his club on Monday.
Press Association Sport understands the Baggies are believed to be aggravated by the north London club’s approach, with Spurs’ last bid on Tuesday understood to rise to £21million only with a series of lengthy add-ons and clauses.
Albion chairman Jeremy Peace has maintained Albion are not looking to sell the 22-year-old, and his resolve has not been broken by Tottenham’s opening offers.
There needs to be a huge change from Spurs for the deal to happen, but former Redknapp expects Berahino to eventually move to White Hart Lane.
“It’s only a game of poker at the moment between (Tottenham chairman) Daniel Levy and Jeremy Peace,” former Tottenham boss Redknapp told talkSPORT.
“Jeremy Peace holds all the aces in that situation because Tottenham are desperate for a striker – he’s the one they’ve identified, so I think the deal will happen before the deadline.
“Everything’s probably all done with the player behind the scenes. He probably has a good idea about where he’s going to live, even.
“All it is now is a game of bluff between the two chairmen, who are trying to get the best deal for their clubs.
“In this case, and in Everton’s case with John Stones, the aces are held by the clubs with the players, because they are two players who are really wanted and they’ll squeeze another million or two out of the deal, for sure.
“Spurs need something at the moment and Berahino’s a good young player, there’s no doubt about that.
“I think it’s a good deal for both clubs and I don’t think (West Brom manager) Tony Pulis is going to lose any sleep over losing him.
“He’s got a few strikers at the club and he’ll be quite happy now to take the money and not have an unhappy man at his club.”