Gayle took issue with Quartermain's tweet, responding with a post to his 2.76 million followers on Tuesday.
This situation escalated on Wednesday morning when Quartermain hit out at Gayle on a Sydney radio show.
"He took it a bit the wrong way, it was only a bit of tongue in cheek stuff," Quartermain said of Gayle's reaction to the tweet. "Then he put that out and all his nuffy followers started trolling me.
"I've been copping a bit of heat but you know what? I couldn't give a stuff.
"Chris Gayle hardly covered himself in glory here while he was in Australia."
Gayle ended a turbulent Big Bash stint with the Melbourne Renegades on Monday night when he equalled the world record for the fastest Twenty20 half-century - off just 12 balls - against the Adelaide Strikers.
In a video released by the Renegades on Tuesday, Gayle said he wanted to return to again play in the BBL despite reports Cricket Australia were considering not registering the 36-year-old for next season on character grounds.
Quartermain said he'd be happy if Gayle never appeared in the Big Bash again.
"To be honest I don't think he's welcome back," Quartermain said. "Who cares about Chris Gayle? The Renegades didn't make the finals, he had a magnificent innings in his last innings but apart from that he was pretty ordinary. Who cares?"
Asked if he thought Cricket Australia would not allow Gayle to come back, Quartermain said: "I don't know that they will kick him out.
"Depends on when they want to retire him as a T20 player. His record here hasn't been all that good, to be honest. I'm not sure that anyone would bother picking him up now, I doubt they will."
Gayle was taking shots at all his "haters" on Tuesday, also posting a lengthy rant on Instagram aimed for the most part at his fellow cricketers.
"I think a lot of past and present cricketers who smile in front my face could've have there (sic) say In the public when my so call issue was going on, but y'all don't have the BALLs to stand firm when it matters," Gayle's post read.
"But yet when u see me you're like, Chris that's BS against you, it was blown out of proportion.
"Don't tell me, tell the media and public!
"The past cricketer who say I make myself look like a chop, the other who claim I was no good to the youngsters while playing for the thunder, the next one who said he expect that sort of behavior from Chris - Y'all can kiss my 'Black Rass'."
"The fans here have been very supportive," Gayle said. "They have been really, really tremendous.
"I am glad I got the chance to entertain them as much as possible as I can. There has never been a harsh comment - it has been very, very positive from the fans' point of view.
"And the kids absolutely love it and I share a lot of moments with them, so it was very pleasing, that would be the most thing to look back to and give thanks to, the fans - really and truly for the support they have given me.
"The respect was unbelievable.
"Apart from India, Australia is the next place where Chris Gayle can really be that forefront, up-front person wherever you go."
-news.com.au
