The 58-year-old is expected to leave the Silver Arrows at the end of the season with the team's Executive Directors, Toto Wolff and Paddy Lowe, taking over his role.
Although Mercedes' non-Executive Chairman Niki Lauda has voiced his determination to keep Brawn, the Englishman is known to be unhappy with the lack of a clearly-defined management structure in the team which has been on an aggressive recruitment drive over the last couple of years.
Brawn was recruited by Williams as a machinist when he formed his team in 1978 and the 71-year-old says he would be a great addition to his team.
"Naively, perhaps, I am unaware that Ross is available," Sir Frank told Ted Kravitz during Sky F1's coverage of the Abu Dhabi GP.
"When he was with us he was really extraordinarily clever in terms of engineering – he is very gifted – and I am sure he has accumulated infinitely more knowledge, just as much about what not to do as much as what he should be doing. So if he was to come he would be a great addition.
"I wasn't aware he was available. I may now have to contact him and I can say no more.
"The reason I am being hesitant is that I do employ people already and it is very unlikely that we could afford Ross, or that he would want to come to us etc, etc and all I would be doing if we didn't get Ross would be offending everyone at the team already."
Having spent a large part of his career at Benetton and then Ferrari battling against Williams could Brawn really move to his old adversary? Martin Brundle thinks so.
"I don't think it is absolutely out of the question," he commented.
"It could be quite good there next year, Williams have the Mercedes powerplant and it can't be any worse than this year. There are a lot of good people there at Williams, they don't have the financial issues that a lot of other teams have – although they will be keen to keep or be paid off by Pastor Maldonado if he moves on. So it is not the craziest of ideas." Skysports.com