Sarah Barshop of ESPN.com provided comments Gaine made about Clowney, who's set to enter the final year of his rookie deal, during his predraft press conference.
"I won't discuss our negotiations publicly, but I'm optimistic that something can be done," he said.
Clowney is set to make $12.3 million after the Texans picked up his fifth-year option for 2018 last April, per Spotrac. He'd become an unrestricted free agent next offseason if the sides don't come to terms on a new deal and the front office doesn't utilize the franchise tag, but that's an unlikely scenario.
The 25-year-old South Carolina native, who struggled with injuries during the early stages of his career, is coming off his best statistical season. He racked up 59 combined tackles, 9.5 sacks and two forced fumbles while appearing in all 16 games.
That's closer to what the Texans expected when they selected him with the first overall pick in the 2014 draft. Pro Football Focus graded him as the league's No. 13 edge defender.
Last month, Clowney said during a public appearance in Missouri City, Texas, he wanted to work out a new deal to stay with the Texans for the long haul, per Aaron Wilson of the Houston Chronicle.
"Hopefully, they lock me in," he said. "I want to be here forever. I know it will come soon. It would mean a lot. It would be great, something I always dreamed of. I don't want to leave this team. I've been here since the beginning. I want to stay here. I want to finish my career here, so I'm looking forward to that."
In the short term, the Texans have the potential to feature the most dangerous pass-rushing tandem in the NFL if both Clowney and J.J. Watt can stay healthy for the entire 2018 campaign.