The Lions used their franchise tender on the defensive end last offseason but couldn't agree to a long-term contract, setting up the defensive end to test the free-agent market once again.
"I don't know. It depends on the situation, honestly," Avril told the NBC Sports Network in an interview Wednesday. "It depends on why I would be taking less money, first off. I don't know, but we just have to get the numbers going and we'll see. I really don't know if I would take less right now."
Avril, unhappy he wasn't able to receive a long-term deal, didn't sign his one-year, $10.6 million franchise tender until a week after training camp began last season.
He put his chances of remaining with the Lions at 50-50.
"I don't know right now. We're waiting to see what's going to go down. We have a little less than a month to try to figure some things out. Hopefully, we get it done," he said in the interview.
Avril, who will turn 27 on April 8, finished last season with 9.5 sacks, 35 tackles and two forced fumbles.
He has 39.5 career sacks and 16 forced fumbles since 2008 when Detroit drafted him out of Purdue in the third round.
Information from The Associated Press was used in this report.