The 22-year-old, who scored 20 goals last season, has started in both of the Baggies' league games this season.
"We have no interest in selling Saido which is what I have told Spurs chairman Daniel Levy," said Albion chairman Jeremy Peace.
"I know we are living in an age where no club can say 'never' about the possibility of selling a player."
He added: "However, the prospect of selling Saido is simply not on our agenda.
"We are going forward with Saido very much in our plans and still striving to add players to improve the balance of our squad."
The Daily Telegraph reports the offer from Spurs is worth £15m, with Albion valuing Berahino at £25m.
In February, Baggies boss Tony Pulis said he put Berahino "on the naughty step" after the forward said that "he hoped to move on to bigger things".
Berahino, with 14 strikes, was the third top English scorer in the Premier League last season behind Spurs' Harry Kane and QPR striker Charlie Austin.
West Brom have rejected an offer from Tottenham for England Under-21 striker Saido Berahino.