Not for the first time this season stories emerged at the start of the week claiming Brawn would leave the Brackley-based marque at the end of the year.
Although denied by Mercedes at the time, it is a rumour that will not go away until Brawn confirms his intentions for the future, which he has so far declined to do.
Earlier this year Brawn did suggest that when the time was right for him to step aside there would be "a soft handover", with Paddy Lowe the man to fill his shoes following his recruitment from McLaren.
There are also suggestions that with the new powertrain regulations for next season, and with Mercedes one of F1's three manufacturers, they will be at the forefront of any title challenge.
To that end, it would appear foolish for Brawn to decide to walk away when he potentially faces his best opportunity to make Mercedes world champions since the German giant bought out Brawn GP following their 2009 title-winning campaign.
Hamilton, for one, would hate to see Brawn go, as he told Press Association Sport: "I get on really well with Ross and I've had some really good conversations with him.
"Before I made my decision we sat down together and he took me through the team's plans and where the team was going.
"Ross, Niki (Lauda, non-executive chairman) and Dr (Dieter) Zetsche (chairman of Daimler AG and head of Mercedes-Benz Cars) were all very influential on bringing me to the team.
"He's a great boss and I'm enjoying working with him. I don't know what his plans are for the future, but of course I'd like him to stay."
Asked if he would tell Brawn not to go, Hamilton added: "I'm sure that helps. I'm sure that can help."
Team-mate Nico Rosberg echoed Hamilton's sentiments as he said: "For the team and me it would be great if he stayed.
"I get on well with him, and he's a great team principal, which is all down to his approach and personality as a team leader. People respect him and he respects people. It works both ways.
"Then there is the mentality he puts into the team. He's very strong and competent.
"At the same time I have confidence in the team leadership's ability to make sure we have a solid future whatever his decision is because we have a lot of great strength in the team now as it is."
In working under Ron Dennis and Martin Whitmarsh at McLaren, and now Brawn, Hamilton has had the privilege of working with a trio of the sport's finest team leaders.
The 28-year-old refused to compare the trio, particularly given his close links to Dennis and Whitmarsh after signing for McLaren at the age of 13.
"I grew up with Ron being an incredible mentor in my life and, of course, Martin was equally a part of that as well," added Hamilton.
"Ron was the one who first saw me but then Martin was the one who took control of my direction, with me moving into Formula Three and the steps I took from there.
"Both were very much like parents to me.
"In arriving at a new team with a new boss in Ross, I've discovered he's a very friendly guy.
"I grew up watching him on TV so I had no idea what his personality was like, but he's been just as I thought of him watching TV.
"He's a very easy going guy, very approachable, and is very much responsible for where the team is today and the atmosphere he has helped create.
"On the technical side he understands everything about the car, he is in all the briefings and meetings, and he always has input.
"The one thing I particularly noticed about Martin, as an engineer, he had understanding of all the technical aspects and designs and stuff like that.
"Ross has that as well but also more on the strategy and how to build a team. That's where I see his strengths."