The Wales international has been constantly linked with a move to Real Madrid, with the Spanish giants said to have offered 100 million euros (£86m) for the 24-year-old.
And the Spurs board member has conceded that the club cannot force the winger to stay if he desires to move to Spain.
However, the 63-year-old has stated that the north London-based club have not yet given up on retaining the player's services despite the obvious appeal of playing Champions League football in Madrid.
“We want Gareth to stay,” he told reporters. “But if a player is desperate to leave, it is very difficult to force him to stay.
“We’ve seen the same thing with other clubs.
“Even if you have an existing contract, you cannot force anyone to play for you.
"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."
Bale arrived at Tottenham's training ground on Tuesday, despite reports in Spain that he would stay away from training.
Spurs manager Andre Villas-Boas gave his squad the day off yesterday following their 5-2 defeat in Monaco last weekend.
Bale's agent, Jonathan Barnett, has denied speaking to Spanish newspaper AS, which on Monday morning reported him as saying that his client could stay away from training after being angered by Villas-Boas' claim, at a press conference in Monaco, that the Welshman would not be sold to Real. Such a move from Bale would be completely out of character.
Bale has not played for Spurs since their first game of the summer - a 1-1 draw against Swindon on July 16.
The forward, who scored a staggering 26 goals for Tottenham last year, missed the club's pre-season tour of Hong Kong because of a gluteal injury and did not travel to Monaco after suffering a foot problem.
Real Madrid coach Carlo Ancelotti revealed last week that the nine-time European champions were in talks with Spurs over the possible signing of Bale.
Having stumped up £33m to sign Luka Modric last summer after weeks of wrangling, Real know all too well how tough a negotiator Tottenham chairman Daniel Levy is.
Unlike team-mates Sergio Ramos and Iker Casillas, who have both spoken publicly about Bale's proposed move to the Bernabeu, Ronaldo would not discuss whether he thought such an astronomical fee for the Tottenham star would be good value.
"In terms of the transfer fee, you should speak to the coach [Ancelotti] and president [Florentino Perez] about that," Ronaldo said at a press conference in Miami.
"I have my opinion, but I'm not going to reveal it in front of the cameras."
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- Real Madrid