Sources say the London network agency is in a state of turmoil, with many staff fearing for their own jobs if the deal, which would see BMB merged with the Omnicom agency, goes through.
Lindsay, the TBWA\UK president, is understood not to have been involved in the acquisition conversations, leading to speculation that he would not be involved in future plans should the acquisition go ahead.
Global TBWA sources have confirmed that talks are taking place, but played down any suggestion that a conclusion was imminent.
BMB, meanwhile, confirmed it has held talks with interested parties, but denied that any deal had been done.
It is thought that Omnicom is attracted by the strength of the senior management at BMB, which was set up in 2005 by the former TBWA\London management team of Trevor Beattie, Andrew McGuinness and Bil Bungay.
A successful acquisition would see the BMB founders return to run the agency they left only three years ago.
Since their resignation, TBWA\London has lost the advertising accounts for McCain and French Connection to BMB.