"We haven't had any bids for Jermain and I suppose if there had been a bid for him, I would have turned it down," Allardyce told reporters at his pre-match news conference ahead of Saturday's FA Cup third round tie against Arsenal.
"Unless it had been that big a bid that the owner told me we couldn't afford to turn it down. Every club has that scenario but we haven't had a bid for Jermain and we don't want to sell him."
Defoe has found the back of the net nine times this season in all competitions for Sunderland, and grabbed a brace against Aston Villa on Saturday to hand his relegation-threatened side a much needed three points.
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The Black Cats are 19th in the table on 15 points from 20 games.
Speaking on Thursday, Allardyce said Defoe's performance had convinced him the forward could lead the line for Sunderland on his own.
"There's always been a belief that maybe he can't play up front on his own but he's played on his own a couple of times for me now and I'm more than willing to continue down that line," Allardyce said.
"If he can continue being as good, and as clinical as he was last weekend, then long may it last."
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
