Video footage showed Zampa putting his hand into his pocket before rubbing the ball prior to bowling the 24th over.
Zampa's team mates Steve Smith and David Warner have just returned to the national setup after serving 12-month bans for their roles in a ball-tampering scandal in South Africa early last year.
"I haven't seen the photos, but I know that he has hand warmers in his pocket," Finch told reporters. "He has them every single game he plays.
"I honestly haven't seen them (the images), so I can't comment too much on it. But I know for a fact that he has hand warmers every game."
Australia next play Pakistan in Taunton on Wednesday.