The 16-year-old was on the bench for their game with Chelsea last month and would have become the youngest player in Premier League history had he come on.
The England youth international is reportedly a target for a host of clubs, with both Chelsea and Arsenal strongly linked.
However, responding to questions about Brown - Clarke insists that the club are not contemplating selling him.
"Izzy is not for sale, let's make that very clear," Clarke said.
"He's done fantastic and has come through the youth team, quickly into the Under-21s, and has put on some really good performances recently."