Once upon a time, many, many years ago (okay, about 20), a young Glasgow band whose musical beauty was admired all across the land were wooed by an esteemed suitor, offering to whisk them away on a tour of the nation's larger indoor venues. But the fair young Belle & Sebastian said no because they weren't quite ready to support a group as righteous and respected as Radiohead.

These days, it's a different story, and the Belles, now a lean, mean live machine, were easily persuaded to join Radiohead on the bill of TRNSMT, the forthcoming three-day non-camping happening on Glasgow Green, brought to you by the makers of T In The Park.

'They said to us that Radiohead had personally requested that we be on the bill with them,' says keyboard player Chris Geddes. 'Whether that is actually true, I don't know … '

'It's really nice to know you have fans in high places,' says singer and multi-instrumentalist Sarah Martin. 'I saw Radiohead really early on in King Tut's, but they're not the sort of band that works that well in a little venue and, sure enough, it turns out they are a stadium band.'

Belle & Sebastian have never played at T In The Park – 'by the time it was viable, I was too old to camp in a ditch,' deadpans Martin – but they are known for their civic-mindedness and love of parks, having organised their own festival in Glasgow's Botanic Gardens in 2004 and rechristened the Kelvingrove Bandstand ten years later with a concert celebrating the opening of the Commonwealth Games.

Since then, they have released the groovy Girls In Peacetime Want to Dance album, performed their biggest hometown concert at the Hydro (turns out Belle & Sebastian are not an arena band), celebrated the 20th anniversary of their seminal debut Tigermilk and spent time in the recording studios of their home city, polishing a number of songs to be released on a trio of EPs later this year.

A couple of band members now have young families, so the decision to do some home recording was mainly a practical one – although Geddes, also known for his DJ gigs around town, finds parallels in his extensive record collection.

'A lot of the music that I really like, stuff from Memphis or Detroit, was just made by people who went into the studio and worked every day in their hometown,' he says. 'It's what we did in the early days when we were in Cava Studios all the time or recording stuff up at Stuart's church hall [frontman Stuart Murdoch lived above a church hall when the band were starting out]. It's nice for us to be back in that way of working.'

Keen Belle & Sebastian watchers will spot the historical link with the three EPs – 'Dog On Wheels', 'Lazy Line Painter Jane' and '3 . . 6 . . 9 Seconds of Light' – which the band released in 1997, containing some of their best-loved songs.

'I think we all feel that a lot of the best stuff we did was on some of those EPs,' says Geddes. 'At the time it seemed the four-track 12-inch was a classic indie format.'

'When we first put out those EPs, we weren't really a proper band, so that was an exciting document of a transitional period of people growing into an entity,' says Martin. 'I wonder if this will end up being a document of a transitional period? I suppose you only really know from the other side, don't you?'

'Thinking of it as EPs rather than an album gave it more of an anything-goes idea that things didn't have to fit so rigidly into an album structure,' says Geddes.

'But that's not quite how it's worked out,' adds Martin. 'It's gone through a lot of conceptualisation. I think at one point the notion was to deal with major faith systems and have one that would represent a Buddhist thing, one that would represent Islam and one that would represent Christianity, and then that quite quickly got moved away from.'

While there is still recording, production and general curatorial work to be done on the EPs, it seems likely that they will feature material written by all the band members, including contributions from Geddes and bassist Bob Kildea. Martin also confirms that a title has been chosen: 'How to Solve Our Human Problems Pts 1, 2 & 3'.

'I suppose most of the songs do concern little problems that people have been preoccupied by,' says Martin. 'I don't know whether we have any clear answers, but I don't think anybody does really.'

She does, however, have some sage encouragement for local audiences at TRNSMT. 'If you can walk home from a festival, then you're laughing … '

Belle & Sebastian play TRNSMT, Glasgow Green, Fri 7 Jul.