However, Rapoport noted the Chargers made "no immediate move" as they continue to evaluate their options behind starting quarterback Philip Rivers.
"It was a good workout," a Chargers source told ESPN's Josina Anderson. "We r still weighing all of our options before camp..We are always looking to upgrade.
"Young man can move," the source added. "He's athletic, threw t/ ball well..but he's not the only QB avab. Not sure we'll add another QB or not."
Kellen Clemens has spent the last three seasons with the Chargers, but Griffin would represent a higher upside backup possibility behind Philip Rivers.
However, he also packs serious bust potential.
That much was clear last season when Griffin went 1-4 in five starts with the Cleveland Browns.
During that abbreviated stretch under center, the former No. 2 overall pick completed 59.2 percent of his passes for 886 yards, two touchdowns and three interceptions while averaging a career-low 6.0 yards gained per pass attempt.
Clemens, meanwhile, has not started a game since joining the Chargers in 2014. Instead, he's been limited to six completions for 73 yards and a score in mop-up duty.