"Probably won't be there first day, that's for sure," Avril told ESPN. "I have to sit down with my agent and figure out when's a good time, if we're even gonna show up."
When asked what goes into his decision process, Avril said there were "a lot of factors."
"This is probably one of the only times in your career that you'll ever get a chance to, you know, opt out (and say) I'm not going to camp or whatnot," he told ESPN. "But it also goes into with injuries and stuff like that. You know, you don't want to get hurt."
The Lions tagged Avril as their franchise player in March, but the sides could not come to terms on a long-term deal before Monday afternoon's deadline.
If Avril, who has yet to sign the franchise tender, chooses to play this season, it must be under a one-year, $10.6 million contract.
Lions veterans are scheduled to report to training camp July 26.
Avril told The Associated Press on Monday that he was not mad at the team for failing to get a deal done.
"Business is business. You can't take it personal," he said.
Lions president Tom Lewand said in a statement the team had "extensive discussions" with Avril and his representative, but the former third-round pick said he wasn't encouraged by the tone of negotiations Sunday night and Monday morning.
"There was a stretch of talks, but I knew in my head it wasn't going to happen," Avril told AP Monday.
Avril was hoping to be rewarded with a long-term contract for being a consistent playmaker for an improving team.
He is the only NFL player with at least 19½ sacks, nine deflected passes, seven forced fumbles and four fumble recoveries the previous two years.
When the Lions snapped their 11-season postseason drought last year, Avril had career highs with 11 sacks, six forced fumbles and three fumble recoveries. He has had 30 career sacks and 14 forced fumbles since 2008, when Detroit drafted him out of Purdue.
Buffalo gave defensive end Mario Williams a $100 million, six-year contract -- with $50 million guaranteed -- when he hit the market this year with fewer than 10 sacks the past three seasons and 53 over his six-year career.
Arizona rewarded defensive end Calais Campbell this offseason with a $55 million, five-year deal after he had no more than eight sacks the past three seasons and 21 in his four-year career.
Information from The Associated Press contributed to this report.