Gayle, 36, was responding to a question from channel Ten's Melanie McLaughlin about his aggressive batting style after scoring 41 runs off 15 deliveries in Melbourne Renegades' victory over the Hobart Hurricanes.
McLaughlin began by asking him about his innings but Gayle quickly steered the conversation away from cricket.
"I just wanted to have an interview with you as well, that's why I batted so well. Your eyes are beautiful, hopefully we can win this game and then we can have a drink after as well. Don't blush, baby," Gayle said.
McLaughlin attempted to laugh it off by saying: "I'm not blushing."
Following the interview, social media was buzzing about Gayle's comments.
BBL head Anthony Everhard tweeted: "I heard Chris' comments and they're disrespectful and simply inappropriate. We'll certainly be talking to him and the Renegades about it."
"This league is all about its appeal to kids, families and females. There's just no place in the BBL - or for that matter cricket anywhere - for that sort of behaviour."
Former England all-rounder Andrew Flintoff tweeted, "Well played McLaughlin!! Big fan of Gayle, but made himself look a bit of a chop there."