Verner, one of the top defensive backs on the open market this offseason, told The Tennessean that he will not accept a "super small" contract offer from the Titans.
"I love being here," Verner told the newspaper. "I love my teammates and I love Tennessee. When it comes to the money, it is not like I need to be paid super high.
"But I am not going to be a fool and take anything that is super small. From a business standpoint, you don't know how long you are going to play in this league, so you have to take advantage when you can."
The Titans are projected to have just over $13 million in salary cap space this offseason, according to ESPN Stats & Information.
"It is not like I want the Titans to spend all of their salary cap just to keep me," Verner told the paper. "It is not like I need $10 [million] or I need $11 [million], or I need to be one of the top five highest-paid corners in the league. I want them to be able to sign other guys to help the team.
"But I also want to feel respected, and the way Tennessee has operated and the way they have paid veteran players, they have set the tempo on how they value players. So if they don't offer me something that shows they value me, I feel like it is a slap in my face."
Verner was the lone Pro Bowl selection for the Titans last season and was a second-team All-Pro after leading the team with five interceptions and 26 passes defensed.
The Titans considered him a better zone than man-to-man corner, and the bigger, faster Tommie Campbell was given every chance to unseat Verner heading into 2013.
But Verner won the job with ease and was a key piece of the secondary, the best unit on the team. The 25-year-old was a fourth-round draft pick in 2010.
ESPN.com Titans reporter Paul Kuharsky contributed to this report.