Ex-NFL star Vernon Davis says it's still a mystery as to how exactly his brother, Vontae Davis, died earlier this week ... although he said Monday he believes the former Colts cornerback passed away following a session in a sauna.

The ex-San Francisco 49ers tight end broke his silence on his little bro's death during an interview with The Daily Mail on Wednesday ... just two days after Vontae was found deceased inside a gym at his Southwest Ranches, Fla. home.

Vernon says he believes his brother either collapsed or slipped after spending time soaking in steam -- but outside of that, he really is unsure of how the former NFLer passed at just 35 years old.

"I'm leaning on the detectives to figure it out, but right now we have no answers," Vernon said. "They are going to run tests and they said they'll get back to us."

"It could be as long as a month, a month and a half, until we know anything."

Vernon told the outlet he doesn't believe drugs had a role, and -- like Davie Police Dept. investigators -- he doesn't think any sort of foul play was involved either.

In fact, from everything Vernon had seen recently, Vontae was completely healthy.

The former TE said he had just linked up with his bro two weeks ago, and he appeared keen on keeping his body in tip-top shape.

"He had the massage therapist there," Vernon said. "He had a stretch therapist, a chiropractor, you name it."