"I think it's fine (playing under the tag)," Henry told SiriusXM NFL Radio on Saturday. "Obviously, I think I would like to get something done just for security and long term and just with the team and the franchise. It's another year of playing football, man, that's how I look at it."
The Chargers and Henry have been negotiating, but there hasn't been any recent progress.
"There were (talks) a while back, but we haven't really done much since," he said. "Hopefully we can get something going this summer, and get it going that way."
Henry signed the franchise tag worth $10.6 million in April. The deadline for franchise-tagged players to sign a long-term contract extension is July 15.
The 25-year-old's expectations for Los Angeles in 2020 are high, and he thinks the arrival of quarterback Justin Herbert will help the club immediately, even if the first-round rookie is veteran Tyrod Taylor's backup to start the season.
"I know there will probably be an open competition and that'll be good for everybody in that room," Henry said. "It'll push each one of those guys."
Coming off a torn ACL in 2018, Henry set career highs with 55 receptions for 652 yards over 12 games last season. He also amassed five touchdown catches.