The 22-year-old forward has been the subject of two rejected bids from Tottenham and seen a transfer request turned down, but speculation has persisted that he could soon be plying his trade at White Hart Lane.
But Baggies chairman Peace has moved to end such talk by revealing he has spoken to the player and told him he is staying put.
“I have informed Saido that he will not be transferred during this summer window and that he is staying at the club,” he said in a statement.
“As I have made clear from the moment Tottenham lodged their first bid for Saido on August 18, selling our top goalscorer was never on our agenda this summer.”
“Our plans have always been based on Saido being part of our squad for the 2015-16 season.
“But there are two other good reasons why he will not be sold.
“Firstly, had we ever entertained the notion of selling him we have not received an offer anywhere near attractive enough from Tottenham Hotspur.
“Not only have the offers been too low as a valuation of the player, but they have been based on stage-payments and add-ons over a long period which do nothing to reflect Saido’s ability and potential.”
Peace was also critical of the timing of Spurs’ bids.
Peace added: “I have the greatest respect for Daniel Levy but he must surely appreciate we would have needed to replace Saido had he left and no consideration of that position has been reflected by Tottenham’s strategy.
“It has contributed to our completing our last two games without a key player.
“I have spoken to Saido and of course I have sympathy for him. He has been unsettled and distracted by all this and I understand that.
“But I have strongly advised him to put this behind him and get back to what he does best which is to work hard for the team and score goals for Albion.”