The Nine Network reported on Thursday that Brennan said the concern came when two layers of tape were applied to the bat.
Allardice said the ICC has no evidence to suggest that players were attempting to cheat.
However, he indicated they would investigate the claims that coatings, stickers and tape on bats could help avoid detection on HotSpot.
Allardice said he had advised Brennan not to imply Australian and England players were trying to cheat.
"I think we did warn him that if he made a statement along those lines, if the inference was that the players were trying to cheat the HotSpot system, he would need some strong evidence to support that," Allardice said.
"Players have had coatings on bats, and manufacturers' stickers on bats, and reinforcing tape on bats for forever and a day."
It's been a highly controversial series, where the HotSpot technology has failed to pick up a number of nicks.
Curtain University in Perth have also conducted research into the thermal imaging process, concluding that silicone tape does have the capability of disguising edges on HotSpot.
Dr Masood Khan said the plastic-based tape can alter how small nicks show up on the infra-red imaging process.
- AAP