12:38 PM PT -- ESPN issued a statement ... saying, "LaVar Ball’s comment to Molly Qerim Rose was completely inappropriate and we made him aware of that."

LaVar Ball is adamant the comments he made on-air to ESPN's Molly Qerim on Monday were not intended to be "sexual in nature" ... despite the way it sounded on live TV.

The head of the Big Baller Brand appeared on "First Take" to discuss the blockbuster trade that sent his son, Lonzo Ball, from the L.A. Lakers to the New Orleans Pelicans ... when things went off the rails.

When Molly asked LaVar if she could "switch gears" and pivot to another topic, LaVar responded, "You can switch gears with me anytime."

Several people condemned the comments, including ex-ESPN star Jemele Hill ... saying, "Kudos to Molly [Qerim] for the professional way she handled LaVar Ball after his inappropriate comment. Maybe ESPN will have finally learned its lesson about putting him on TV."

Now, LaVar's rep, Denise White, is issuing a statement from the BBB camp ... saying, "[LaVar] was asked if he wanted to switch gears, in his mind switching gears was 'changing the subject anytime' and he said, 'yes, you can switch gears with me anytime.' At NO time was that intended or meant to be sexual in nature."

This isn't the first time LaVar has been under fire for comments he made on-air to a woman -- back in 2017, he told FS1's Kristine Leahy to "stay in your lane" after she questioned him about his parenting style.