It was confirmed this week that the UK would host the 2023 edition due to the current conflict in Ukraine, who won the 2022 competition and would therefore traditionally host the following year.
As the UK finished second with Sam Ryder's song Space Man, the country has been given the opportunity to select a host city for the competition.
BBC News at Ten anchorman Edwards responded to a tweet by Welsh journalist Grant Tucker suggesting that the Principality Stadium in Cardiff would be an ideal venue for the 2023 contest.
— Huw Edwards (@thehuwedwards) July 25, 2022
— Huw Edwards (@thehuwedwards) July 26, 2022
Edwards wrote: "This is so obviously right, and your presenter is standing by."
In a subsequent tweet, Edwards suggested that the campaign to have him installed as the Eurovision host could be called "Huwrovision 2023".
Watch: UK will host Eurovision Song Contest on behalf of Ukraine
Numerous cities have declared on social media that they would like to submit a bid to host Eurovision 2023 and the European Broadcasting Union announced they had been contacted by 16 cities.
Cardiff is in the list of cities to formally express their intention to bid, along with locations including Manchester, London, Birmingham, Newcastle, Glasgow, Nottingham and Belfast.
Edwards turned 60 last year and said in an interview that he is pondering his future as a nightly news anchor on the BBC.
He said: "I don't think I'll be doing that for long. Because I believe that, in the first place, I think it's fair for the viewers to get a change.
"Secondly, I have co-workers who are very talented. It's time to give them a chance too."
Edwards has fronted the News at Ten since 2003 and recently took over from David Dimbleby as the lead anchor of the BBC's election night coverage.
Watch: Huw Edwards takes break for croissant during election coverage