The band referenced the singer and his Smiths-era songwriting partner Johnny Marr in their track '1985' from the 2004 album Lifeblood.
Speaking to BBC Radio 2, bassist Nicky Wire and frontman James Dean Bradfield revealed that they recently met three of their favourite '80s artists after speaking to Mike Scott of The Waterboys, Jim Kerr of Simple Minds and Ian McCulloch of Echo & The Bunnymen.
Wire said: "There's only Morrissey left, because they were the four of our great icons of the '80s, really."
Bradfield added: "The unobtainable Morrissey, probably."
Wire responded: "You never know."
Morrissey was this week announced as the headliner of the Hop Farm Festival in Kent.