The brothers, who say they are innocent, are accused of having formed an organised criminal network in early 2021 in Romania, as well as in the US and Britain
"If I was going to run a team I'd like to have Ron with me," the Briton told Reuters at the US Grand Prix, which Dennis attended 50 years on from his first involvement at a race weekend.
"I think he does a good job. Anyone that chucks him out is stupid. He's dedicated. I think we ought to try and support him so they don't get rid of him," added Ecclestone, who will turn 86 in Mexico next Sunday. "It would be a shame to see him go. He's one of the good old timers."
Britain's autosport.com website said in an unsourced report last week that Dennis, 69, would be leaving as McLaren chairman and chief executive at the end of the year when his contract expired.
A McLaren spokesman said in response that Dennis, who attended his first Formula One race as a Cooper mechanic in Mexico in 1966, had stated "categorically" that he is not stepping down.
"Moreover, he remains contracted as chairman and chief executive officer of McLaren Technology Group and he retains a 25 percent shareholding - exactly equal to that of (Saudi-born business partner) Mansour Ojjeh."
Mahmood al-Kooheji, CEO of Bahrain's sovereign wealth fund Mumtalakat, which owns the other 50 percent, told Reuters they had "great admiration" for Dennis.
"He's a colleague, an inspirational chairman who is behind all the ideas," he said. "Whatever he decides, we will support his decision. I hope he continues and I will try to make him stay."
However, former McLaren driver turned television commentator Martin Brundle said he expected Dennis to leave.
"There seems to have been some friction and there seems to be a new direction they want to go in," he told Sky Sports television.
"I don't know who they've got in mind and (in) which elements of McLaren they will make changes, and whether they will restructure. We'll have to wait and see."
Dennis, who has been involved with McLaren since 1980, stood down as team boss in 2009 but returned as group chief executive in January 2014.
The brothers, who say they are innocent, are accused of having formed an organised criminal network in early 2021 in Romania, as well as in the US and Britain
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