The 22-year-old former Real Madrid full-back was the subject of a transfer bid from Serie A outfit Fiorentina this week that was turned down by Wanderers.
Alonso's current deal at the Reebok Stadium expires in the summer but, speaking ahead of Saturday's FA Cup clash with Everton, Freedman confirmed the players has passed up the opportunity to pen an extension.
"We had a bid for Marcos from Fiorentina which was rejected," Freedman said. "It was nowhere near the value we think he's worth.
"I told the young guy that we don't want to sell him.
"We've offered him a new contract which he's rejected, so everything's put to one side and we concentrate on the football now."
Alonso has established himself as a fixture in Freedman's first XI during recent weeks, starting Bolton's last six matches in all competitions.
- Sports & Recreation