Mark Knopfler rejected the opportunity to reform Dire Straits, according to the band's bassist John Illsley.
Speaking to the BBC, Illsley admitted he would "love to do" a reunion tour but had not yet been able to convince Knopfler to return to the road with tracks such as Money for Nothing and Brothers in Arms.
Illsley said discussions on a reunion -13 years after the band's official breakup - had taken place "from time to time".
"He [Knopfler] says 'Oh, I don't know whether to start getting all that stuff back together again'," he added.
"I think we've definitely got one more tour left in us, and probably another record too.
"But he's doing incredibly well as a solo artist, so hats off to him. He's having a perfectly good time doing what he's doing."
Speaking at the Hay on Wye Literary Festival last year, Knopfler said he did not miss the celebrity that came with Dire Straits' multimillion-selling success.
"It just got too big," he explained.
"If anyone can tell me one good thing about fame, I'd be very interested to hear it."
Illsley added that he was "very open" to any form of reunion.