Berahino is the Premier League's top-scoring Englishman this term with seven goals to his name from 11 outings.
That form has seen the 21-year-old called up by England manager Roy Hodgson - a former Albion manager - for the first time for upcoming fixtures with Slovenia and Scotland.
It has also resulted in several media reports claiming a number of England's elite clubs may look to the Burundi-born striker when the transfer window re-opens in January.
Berahino last week stated that he may have to leave The Hawthorns to fulfil his ambitions for club and country.
However, Albion chairman Jeremy Peace insists the club will not entertain any offers for their star man, and revealed talks have begun over improving the terms of Berahino's current West Brom deal, which has three and a half years left to run.
Peace told the club's official website: "I wish to assure our supporters that Saido Berahino will not be going anywhere in January or, I hope, next summer.
"It is not in our minds at all to trade a footballer the club has worked so diligently to develop.
"He is contracted to play for West Bromwich Albion until at least the summer of 2017 and we are happy to sit down with him and discuss extending that commitment on terms which recognise his continuing improvement as a footballer and his growing importance to our own plans.
"We have begun that process by opening preliminary talks with Saido's representatives.
"We are delighted that this development has now taken him all the way to the senior England squad.
"This reflects proudly on our club and the efforts of all the staff who have played such a key role in Saido's progress since he arrived here as an 11-year-old."
