London, Manchester, Glasgow, Liverpool and Leeds are also possible host cities.
The Welsh capital is one of many cities being touted following confirmation on Monday that the United Kingdom will host the event in 2023 on behalf of Ukraine.
Organisers the European Broadcasting Union (EBU) decided the event could not be held in the war-torn country following the Russian invasion.
Baker was part of Bucks Fizz alongside Bobby G, Mike Nolan and Jay Aston when they triumphed at Eurovision in 1981, winning with their song Making Your Mind Up.
Speaking on BBC Breakfast, Baker, 68, said: “It needs to go to a city where there’s an international airport, where they’ve got a venue that’s big enough, where there are enough hotels, so any one of those would work.
“I think it would be nice if it didn’t go to London although, for me, I live in Kent, I’m half an hour from London. So for me, that will be perfect.
“But would be nice if it went to (a) regional… I fancy Cardiff, I think that would be nice. Like you say, the Land of Song.”
Welsh Secretary Robert Buckland also added his voice to calls for Cardiff as the host, telling reporters: “I’m a fan of Eurovision and I think it’d be great to see it here in Wales, the Land of Song.”
He added: “I think Cardiff would be a great venue because it’s got the capacity.
“The reality is there are only a few places in the UK that have the capacity, there has been talking about the Manchester Arena, Glasgow.
“It seems to me that there’s a consensus that needs to be out of London, which is a good start, and therefore I think Cardiff definitely needs to be in the running as a major international venue, not just for sporting events, but for cultural events, as well.
“I can’t think of a better venue for a cultural event of this magnitude than Cardiff so I think we should go for it. And I would urge the BBC to work on that basis.”
Bucks Fizz relaunched as The Fizz a few years ago after changing their name because of a legal row with former member Bobby G, and reformed with original members Aston, Baker, Nolan and newest recruit Bobby McVay, who represented the UK at Eurovision in 1983.
Ukraine will automatically qualify for the grand final alongside the so-called big five nations, the UK, France, Germany, Italy and Spain, who get a free pass because of their financial contributions to the event.
It will be the ninth time Eurovision has taken place in the UK – more than any other country.
The bidding process to select a host city will begin this week, with the BBC and EBU jointly making the final decision.
Asked about the significance of the competition coming to the UK, Baker said: “I think it’s fantastic. I mean, it’s the biggest musical extravaganza in the world and it happens once a year and it’s coming to the UK.
“And I think actually as well, we came second to the Ukraine, it kind of makes sense that it comes here rather than anywhere else.
“Obviously, it can’t go to Ukraine, and I think it would be lovely for us to host it on behalf of Ukraine.
“As long as the Ukraine are completely involved, as long as their presenters, we’ve basically given them the shell to do it in my opinion, I think their production teams and their presenters and everything should be totally involved.
“It’s just like we’re giving them the venue to use, that’s what I think.”
It comes as several of Britain’s major cities, including London, Manchester, Glasgow, Liverpool and Leeds, threw their hat into the ring to host Eurovision on Monday.
Claire McColgan, director of Culture Liverpool, told Good Morning Britain that the city, which was given Unesco City of Music status in 2016, said the “thought of Liverpool doing it with the compassion that Liverpool people have and the fact that we could fill every single part of this city with brilliant music, but also do loads of community work and schools work like we do with all our big events, would just be a wonderful opportunity for Liverpool.”
Asked about the funding and short lead time for preparation, she said: “I think the kind of key thing about Liverpool is we did the events research programme, where we opened up the first nightclub, we opened up the first festival during Covid, we work very quickly.
“And Liverpool has got an infrastructure, where we can put an event on in a really short time that the event is really impactful as well.
“So we can shut the whole city down. So even though the show itself is in the arena, we’ve got all these kind of iconic spaces that are known across the world… we could just do some really, really beautiful things that I don’t think any other city could do.”
Fellow former Eurovision winner Lulu, 73, called for the contest to be held in her home city of Glasgow.
Speaking on BBC Newsnight, she said: “It has to be Glasgow because that’s where I come from.
“They’re so politically savvy, they’re the most fabulous hosts, they absolutely are music mad.
“I think it would be just the most fabulous thing, and I would be there. I just cannot wait.”