The Welsh winger has been linked throughout the close-season with a big-money move to the Spanish giants after an impressive campaign in 2012-13.
Bale hit 30 goals in 53 games for Tottenham as they missed out on UEFA Champions League qualification on the final day, prompting interest from Real.
However, Villas-Boas has made no secret of his desire to keep the 24-year-old, with the Portuguese confirming on Friday that negotiations over a potential new deal are still continuing from last season.
He said: "There were contacts last year between the club and his agent and there are still ongoing contacts between club and agent.
"The player renewed his contract last year by the beginning of the season, if you remember, and it's something that is being dealt with by the chairman and the agent."
While Villas-Boas is optimistic about getting a deal done, he did admit that an agreement is yet to be reached.
"Talks are ongoing, but that doesn't mean there is an agreement," he continued.
"At the moment we are confident. The player is under contract, a good contract at Tottenham, which was done last year.
"It's something we are speaking about but we don't have any further developments."
