Reports have claimed O'Driscoll has been interviewed for the vacancy, along with former Sheffield Wednesday manager Brian Laws, who started his playing career at Burnley.
O'Driscoll has impressed during his time at Doncaster and has guided the club into the Championship on the back of an attractive brand of football.
Ryan does not want to lose the ex-Bournemouth boss, but said he will demand "serious compensation" if O'Driscoll takes the job.
"We don't want to lose Sean, but should it happen we shall be seeking serious compensation," said Ryan in The Sun.
"We've not been called 'the Arsenal of the Championship' for nothing. That's down to Sean."
Doncaster 11/8, Brentford 15/8, Draw 12/5