Highly-rated Brown is a product of the Baggies' youth academy and made his debut for the senior team in their 3-2 defeat to Wigan Athletic at the end of last season.
The 16-year-old has also played for England Under-16s and Under-17s, alerting the attention of Chelsea. However, West Brom insist that the player is not for sale.
"Albion have today rejected an offer from Chelsea for academy product Isaiah Brown," read a statement on the club's official website.
"Under Premier League rules the Baggies are due compensation from the London club for the 16-year-old midfielder, who has been at The Hawthorns for three years and had agreed to sign scholarship forms."
West Brom's sporting and technical director Richard Garlick expressed his disappointment at Chelsea's offer.
"We are disappointed by Chelsea's offer. We have invested a lot of time and money in Isaiah's development as a player and - as one of our most exciting academy products in recent years - we had hoped to bring him through into our first team," said Garlick.
"But Chelsea have forced our hands and we are more than prepared for the matter to be decided by a tribunal if needs be. More importantly, it makes you question why these young players are joining bigger clubs when they are likely to gain more first-team opportunities in the Barclays Premier League at clubs similar to us."
Brown's sole Premier League appearance so far at the age of 16 years and 117 days made him the second-youngest player in the history of the division.