But maybe they aren't as slim as we think.
As Jackson starts negotiating as a free agent -- a process ESPN NFL Insider Adam Schefter said began just minutes after the Eagles made his release official -- he will end up needing the people who know him best to endorse him as a person and a football player to prospective new teams.
There are probably few in the league who know Jackson like Bengals coach Marvin Lewis does.
During a November 2009 pregame news conference, Lewis said he had known Jackson's family for as far back as he could remember.
"I grew up with DeSean's mom," Lewis told reporters at the time. "DeSean's grandfather was my minister as a young kid growing up. He went to Long Beach Poly [high school], and I coached at Long Beach State. So I know everybody there."
Lewis had been asked whether he regretted drafting receiver Jerome Simpson in 2008 instead of Jackson, then a second-year player whose career had gotten off to a strong start. That season, Jackson had a career-high 12 touchdowns for the Eagles. Lewis said he was happy with the way the 2008 draft played out and that he knew quite well what Jackson's capabilities were.
Simpson was picked 46th overall in the 2008 draft. Jackson, who was noted for having character issues at the time, went to Philadelphia 49th overall.
Character will be at the heart of every team's push to sign Jackson. After a NJ.com report surfaced Friday connecting Jackson to gang members in his native Southern California, his character took a heavy blow. One alleged associate in the NJ.com report was charged with murdering a 14-year-old. Minutes after the Eagles announced Jackson's release, Jackson released a statement saying he has never been associated with gang activity and that the reports are "irresponsible and just not true."
Lewis' history with Jackson's family might mean there's a chance the Bengals would debate signing him, but there are few other reasons the franchise ought to even entertain the idea.
For starters, Cincinnati already has a topflight wideout in A.J. Green. The Bengals also have playmakers in receivers Mohamed Sanu and Marvin Jones and tight ends Jermaine Gresham and Tyler Eifert. Sure, Jackson probably would end up becoming the No. 2 receiver in the Bengals' rotation, but that would suddenly shift Jones down to No. 3 after his breakout season, and Sanu to No. 4.
Logistically, there just doesn't seem to be room for Jackson. Add to that the uncertainty of what may be going on in his personal life, and it doesn't seem likely that the Bengals take the chance.
Cincinnati has taken risks on players with off-the-field baggage in the past, but the timing isn't right to do so in this instance. Not only is there a large amount of negative attention on Jackson right now, but the Bengals also are in the middle of an image-rebuilding process that has gone well of late. Once known for being a haven for bad-boy behavior, Cincinnati now boasts a locker room that is the envy of teams across the league.
Maybe Lewis' ties are reason enough for Jackson to be a Bengal, but at this moment, it seems highly unlikely that happens.