A source indicates the physical issue keeping Bengals TE Jermaine Gresham off the field right now is recovery from hernia surgery.— Field Yates (@FieldYates) June 10, 2014
Hopefully, this was a minor procedure that won't affect Gresham's availability for training camp, though hernias are a scary injury to deal with, depending on the severeness of it. He's on the final year of his rookie deal, and needs to have a big season to ensure he gets a good contract offer from either the Bengals or another NFL club.
Gresham is coming career-lows in receptions (46), receiving yards (458) and touchdowns (4) in 2013. Cincinnati spent the 21st-overall pick in the 2013 NFL Draft on Notre Dame TE Tyler Eifert, so they have Gresham's replacement lined up if he leaves, though they'd prefer to keep using their 2-TE sets with Gresham and Eifert.
The team will likely work on a new deal with him once they've got Dalton and Burfict dealt with. Until then, he's playing in a contract year, and the sooner he gets back on the field, the better.
In the meantime, Alex Smith was re-signed to give the Bengals another body at TE in OTAs. He could end up winning the third TE spot by default if Orson Charles remains at fullback. Smith joined the Bengals in 2013 as a blocking TE and caught three passes for 12 yards and one touchdown. He also played some h-back.