I think there is one, but it is limited. If the Jets let Braylon Edwards go, Moss could be a calculated gamble to replace him on a one year deal. Losing Edwards would leave something of a need for a vertical threat. On a one year deal, I think Moss could make sense. I know he did not look very good in 2010, but part of that had to be an inability to find a rhythm playing for three different teams.
Moss is a guy who sometimes lacks motivation. His two biggest years in the league came where he felt like he had something to prove. Those were his rookie year in 1998 when character concerns led him to drop in the Draft and in 2007 when many thought he was done and got traded to the Patriots for a fourth round pick. He admittedly was not 34 then, but he would probably be cheap enough to cut easily if he actually is washed up and/or a problem.
I am not sure other scenarios would make sense, though. I am not sure Moss is diverse enough as a route runner at this point of his career to replace Santonio Holmes as an effective underneath threat. Having an Edwards/Moss/Holmes trio could sound tempting on the surface. Holmes would be deadly out of the slot working on nickles with Edwards and Moss providing deep challenges. I am not sure this would be effective in practice, though. Moss tends to lose his focus if getting him the ball deep is not a focal point.
There are a lot of reasons to not want Randy Moss. Darrelle Revis is right that Moss can be a slouch. He is definitely not my first choice or even my second. I do, however, think there is a scenario where signing him could make sense as a guy to make a defense pay for committing too many men to stop the run. Maybe Rex Ryan could reach him. I at least prefer him to Plaxico Burress, who is just as old and has not played since 2008.
Moss wouldn't have to face Revis in games, which would give him a better chance.