Reports at the weekend had suggested the Premier League trio were battling it out to sign the highly-rated youngster, but Browett has moved to ward off interest, insisting Zaha will be playing Premier League football with Palace before long.
Zaha is an England under-21 international, and has already made 70 Championship starts for Crystal Palace, despite still being in his teenage years.
The 19-year-old has been in red-hot form this season, and has scored four goals in his last two games as Palace have surged up the Championship table.
But the club's co-chairman has assured fans that Zaha will not be sold in Janaury.
Writing on a club forum as CPFC2010, and reported by the Guardian, Browett said: "I can assure you that Wilfried is not 'for sale.' We hope that he'll be playing Premier League football next season. For us.
"Even if that doesn't happen, he's only 19 and still learning his trade in surroundings where he is comfortable and happy. He's on a five-year contract and we really don't need the money."
Zaha was voted the Football League's Young Player of the Year last season, and began to attract the interest of Premier League suitors after a string of eye-catching displays, most notably against Manchester United in the Carling Cup.
Most recently Manchester City, Arsenal and Liverpool were thought to be competing for his signature. Liverpool boss Brendan Rodgers made it clear earlier last week that the Anfield club would have money to spend in January, while Manchester City are believed to be focussing their transfer activity on football's brightest young talents.
And Arsenal boss Arsene Wenger has an excellent record of bringing through young talents, having bought Alex Oxlade-Chamberlain and Theo Walcott through to the Gunners first-team as teenagers.
All three are reportedly keen on Zaha, who has emerged as one of the Championship's most exciting wingers. The 19-year-old was also thought to be a target for Tottenham at one stage, but City, Liverpool and Arsenal are now the frontrunners, according to reports.