He has shown little indication that he would like to retire from the Question Times chair any time soon, but his colleagues have already set their sights firmly on his job.
Kirsty Wark, the Newsnight presenter, has said she will throw her “hat in the ring” for the role, along with “many” other broadcasters.
Dimbleby, who is 79, has chaired Question Time since 1994, has previously said he will continue to “turn up if they want me”, for “as long as I can do it well”.
In an interview with Good Housekeeping magazine, Wark was asked about her ambitions and, specifically, whether she could imagine herself presenting the panel show.
“I think there will be many people when David Dimbleby decides he doesn’t want to do it any longer,” she said. “I think I will be one of them, but I’m sure lots of people will throw their hats in the ring for that.”
The question over who will follow Dimbleby into the Question Time hotseat has been discussed for years, but is likely to take on another dimension after revelations about the gender pay gap at the BBC.
The corporation has already pledged to support more women in senior roles, after accusations that television executives lose interest in female broadcasters as they get older.
Asked about the pay gap, Wark, 63, said: "People were genuinely shocked. There were pay gaps between men and women on different programmes that were outrageous.
"The Today programme was one of them.
"The idea that women should be paid less for doing an equal job is absolutely outrageous and what happened was that either knowingly or unknowingly, the BBC let that grow... and so it is being redressed now and it will have to be redressed."
Wark, who was revealed to be earning between £150,000 and £199,999, said: "We are a public service organisation. It will be changed and the culture will be changed as well. The BBC has to be the standard bearer of equality."
When the figures were unveiled, Radio 2's Chris Evans topped the 2017 list on more than £2 million, while the highest-paid woman was Claudia Winkleman on between £450,000 and £499,999.
Big name stars such as John Humphrys, Huw Edwards, Nicky Campbell, Jon Sopel, Nick Robinson and Jeremy Vine have now reduced their salaries at the BBC.
Wark also spoke about her experience of the menopause, saying that too many women do not get the help that they need from GPs.
"It can be easy, it can be hard, it can be hellish," she said. "I had an abrupt one but what I found so distressing was how many women are fobbed off by their GPs with antidepressants or 'you'll get through it,' when there is all manner of help.
"Also, women weren't talking to each other about it or to their mothers or daughters."
For all her career aspirations, Wark added that being a mother is “the most important thing, it just absolutely is!”
The full interview with Kirsty Wark is published in the July 2018 issue of Good Housekeeping, on sale May 30.