Former assistant manager at Burnley Sam Ellis is now at Leeds, and The Whites have made bids over a £1m for the England U-21 international.
Cotterill, however, believes he is winning the fight to keep the talented 19-year-old.
"He's keen enough to stay that I had dinner with him and his mum and dad last night," Cotterill told Sky Sports News. "At the end of the day, Leeds have made a big bid for Chaplow but their bid falls short of our requirement.
"If somebody comes in with an offer big enough then we have to consider it, for the lad's sake as well. But at this moment in time he's a Burnley player and I don't anticipate him going anywhere else at the moment."