Sources close to Manziel and Griffin told Johnson that each player has long maintained that Jones would be interested if they were cut by their teams.
It's also no secret that Jones wanted to draft Manziel in 2014, and he's admitted to being "a big admirer" of Griffin.
Manziel appeared to be turning a corner in Cleveland after spending 10 weeks in rehab during the offseason for an undisclosed substance abuse issue, but has found himself in trouble several times over the past few months.
The latest incident occurred over the weekend when Manziel failed to show up at the team facility for concussion treatment Sunday after he was reportedly spotted Saturday at a Las Vegas casino.
Browns owner Jimmy Haslam hinted Monday that it may be time for the team to move on from Manziel, noting, "We do have the second pick in the draft."
Griffin, the No. 2 overall pick of the 2012 draft, has been relegated to bench duty in Washington this season after losing the starting job to Kirk Cousins.