The 24-year-old returned to training with Spurs on Tuesday ahead of his club’s decisive talks with Real Madrid, due to take place in the next 48 hours, over the Welshman's potential world record transfer.
Mills reiterated the club's not-for-sale stance, telling the London Evening Standard: "We very much want Bale to stay."
But, when pressed, he added: "If a player is desperate to leave, it’s very difficult to force him to stay. We’ve seen it [at] other clubs. Even if he has a contract, you can’t force somebody to play for you."
Having failed to qualify for this season's Champions League, the director hopes that the north London club can make the step up in the upcoming season following the summer aquisitions of Roberto Soldado, Paulinho and Nacer Chadli, and appreciates the difficulty in keeping star players like Bale without the lure of Europe's premier club competition.
"That’s precisely the issue," he continued. "So this summer, we are investing in a great squad and we hope that provides us with Champions League football next year and we start to win trophies, FA Cups.
"That’s what Tottenham need. We have made some good acquisitions."
Mills also hinted at the possibility of another forward arriving at White Hart Lane following the £25.9 million club record signing of Soldado from Valencia."There are others in the pipeline," he revealed.
"Strikers are very high on [manager] Andre Villas-Boas' list of priorities and Daniel [Levy] is trying hard to make sure we have strength up front. It’s a really exciting time to be at the club.”