But his introduction to the musicians who are currently helping Glasgow-born Knopfler return to his roots led to a new project that has consumed the flamenco guitarist over the past few months and resulted in a new album, Tierra, which Amigo will premiere at Celtic Connections this weekend and follow up with a world tour beginning in March.
Amigo met Knopfler's long-time keyboards player, record producer Guy Fletcher, for the first time backstage in Cordoba, where the Seville-born guitarist now lives, and the pair immediately hit it off. Then, when Amigo heard Scottish fiddler John McCusker and Manchester-born Irish piper, flautist and whistle player Michael McGoldrick, who have been touring and recording with Knopfler over the past two or three years, he decided he had to work with them on some new music.
"I've never been to Scotland or Ireland before and my only experience of Celtic music has been hearing the Chieftains a few times over the years," says Amigo through his interpreter.
"As soon as I heard John and Michael, however, apart from the amazing quality of their playing, I loved the idea that they seemed to sound like the land they come from. There's something in their playing that could only be there if they had these roots and I wanted to mix my land with theirs."
Forty-five-year-old Amigo, who has toured internationally since recording his first album, De Mi Corazon del Aire, in 1991 and has worked with the likes of Bob Dylan, David Bowie, Sting and John McLaughlin and earned special praise from one of his biggest guitar heroes, Pat Metheny (Amigo modestly plays down Metheny's description of him as the greatest guitarist alive as "a mistake"), began composing almost immediately after the Knopfler concert.
In preparation, as well as listening to McCusker and McGoldrick's albums and the latter's work with Capercaillie, Amigo also checked out musicians from the Celtic enclaves in Spain, including the Galician piper Carlos Nunez, to get closer to what for him is a different style of phrasing.
"I was fairly sure our styles of music would blend naturally and when I mentioned this to Guy he agreed, and despite the fact I don't speak English and he doesn't speak much Spanish, he offered to produce the album," says Amigo.
"I've worked in flamenco-jazz fusion projects, which are not so unusual these days, and I've sometimes found the two styles crowd each other out and leave the musicians no space to develop ideas. So I decided I would write themes and let the Celtic players interpret them in their own way.
"It's still my music and has flamenco at its heart but I wanted to give the fiddle, pipes and flute room for the players to express themselves."
Recording Tierra in London took only six days. Fletcher, who has worked with Roxy Music, Mick Jagger, Aztec Camera, Randy Newman and Tina Turner, as well as Dire Straits and Knopfler's subsequent bands, helped Amigo in arranging his compositions and brought in musicians including the widely experienced drummer-percussionist Danny Cummings, Celtic Connections' musical director Donald Shaw on accordion and bassist Ewan Vernal.
"I'm really enthusiastic about this album," says Amigo, "because it has a positive message. It conveys the idea of beauty and a sense of connection to the land of different countries, which is why I called it Tierra. It's a new beginning for me and I've been really moved by the way everybody has put their hearts, as well as their minds and imaginations, into the music.
"Although it's a meeting of two or three or more different cultures, it flowed right from the beginning and it really felt as if it was meant to be because the way it came together was so natural and effortless. I'm looking forward to playing the music on stage now and giving everyone involved their time in the spotlight because they gave so much in creating this new fusion."
Vicente Amigo performs Tierra at Glasgow Royal Concert Hall on Friday.