NEW YORK (CBSNewYork) - Former Vermont Governor Howard Dean is under fire for a Tweet suggesting that Donald Trump's sniffling during the debate may be related to cocaine use.

Trump was heard sniffling repeatedly during Monday night's debate. Social media users took note and had fun with it, but Dean - a former Democratic presidential candidate and former chairman of the Democratic National Committee - took it a step further.

"Notice Trump sniffing all the time. Coke user?" Dean Tweeted.

Speaking on MSNBC Tuesday, Dean refuse to back down.

"You can't make a diagnosis over the television, I would never do that," Dean said. "But he has some interesting - that is actually a signature of people of who use cocaine. I'm not suggest that Trump does."

His interviewer pointed out Dean's Tweet suggests just that.

"So he sniffs during the presentation, which is something that users do. He also has grandiosity, which is something that accompanies that problem. He has delusions - I'm not talking about being crazy - but for example when he told everybody he was very smart for not to pay any taxes and then denied he said it in front of 100 million people, it's not that he's delusory about it, he thinks he's not going to get caught. That is delusional."

"Do I think at 70 years old he has a cocaine problem, probably not, but it's something I think it would be interesting to ask him and see if he ever had a problem with that," Dean added.

The Tweet drew a rebuke from fellow Democrat David Axelrod, a former top advisor to President Barack Obama.

Trump told Fox News Tuesday there were "no sniffles" and he was in good health.

"Maybe it was the mic. There were no allergies, no cold," Trump said.