Cook's captaincy has come under fire in recent weeks, and calls for him to quit his role have grown louder following England's 95-run defeat to India in the second Test at Lord's.
The 29-year-old has stated that he has no intention of stepping down as Test skipper.
"He's obviously not going to move unless you get six wild stallions to pull him out," Boycott told BBC Radio 5 live.
"It's that stubbornness about him. He's only interested in what he sees."
Meanwhile, England coach Peter Moores has insisted that Cook is the right man to lead the team.