With 562 wickets in 139 Tests, Lyon has been one of the standard bearers for his generation and is poised to be Australia's frontline spinner for this winter's blockbuster Ashes against England.
The 37-year-old is well-known for stoking the pre-Ashes flames and suggested at a Cricket Australia function a fortnight ago that Jack Leach is still England's best spinner, adding Bashir "has been OK".
Bashir, currently recovering from surgery on the little finger of his left hand, was unmoved by the jibe, as he told the PA news agency: "Everyone has their own opinions and that's fine.
"I just stick to what I believe and what the people around me believe. I don't really look at that stuff."
Bashir was far more complimentary towards Lyon as the 21-year-old added: "I've never crossed paths with him but I have been watching him since I was young.
"I do enjoy the way he bowls, especially his overspin, it's a great asset he has, and the amount of revs he puts on the ball. He's someone I've been looking at for a while now."
Taller than Lyon at 6ft 4in but with the same wiry frame, Bashir, whose 68 Test wickets have been at a modest average of 39, has been tipped to capitalise on excess bounce often found on Australian pitches.
A reconnaissance mission Down Under last winter yielded just four wickets in five matches for England Lions but Bashir, having worked under Graeme Swann there, feels better prepared for the experience.
Bashir said: "I learned you do get bounce but you've got to find a way to use that. I've got height but there's more than just height to extract bounce from the wicket. Just small technical things.
"It's just (about) nailing what I do best. If you look at my attributes - I'm tall and try to put as many revs on the ball as I can, with that comes variations.
"I'm still learning, still quite young, I'm still trying develop my game and better myself day-by-day. That will never stop. I love talking about the game and I love learning."
Bashir is likely to get his first experience of Ashes cricket on November 21 in Perth, having featured in a hotly-contested series against India this summer where there were a number of flashpoints.
The battle for the urn could see more heated scenes and Bashir, usually a cool customer, insisted he would not be afraid to stand his ground as England look for a first win in Australia since 2010-11.
He said: "Don't be surprised if I do have a word but I genuinely like to keep things cool. If things do get heated then I'm there.
"It would be special and a great achievement (to win the series), especially with this regime at the moment. We're looking forward to what it brings."
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