Property agent NAI Fuller Peiser has confirmed that freeholder Gillette is now in talks with a single party over the Grade II-listed building's future.
This potential deal is thought to involve the Irish-based Regency Hotel Group, although the agent refused to confirm this.
After interviewing seven parties, it is understood that talks are now at an advanced stage with just one consortium.
At one point the building looked set to fall into the hands of Brentford after it had teamed up with developer Active Asset Management. However, John Bowles of NAI Fuller Peiser, said it had failed to make the recent shortlist.
Bowles was keen to stress that a detailed planning brief had been worked up with local conservation officers at Hounslow council and English Heritage.
NAI Fuller Peiser is due to make an announcement about the site's future at the end of October.