The picture showed the duo during a recent workout with Tom Brady holding a training rope that is attached to Edelman’s waist.
Last season’s Super Bowl MVP captioned the picture insisting he wanted some more space from his quarterback.
“After 10 years you’d think I would have a longer leash in the off season @tombrady,” Edelman wrote on Instagram.
Brady was quick to reply to the comment: “Nope!” Said the six-time Super Bowl champion.
Edelman and Brady are not shy from using social media for a bit of banter and recently the 32-year-old wideout graduated from Kent State.
He said he wanted to fulfil a promise he made to his parents a decade ago, while also trying to set a “great example” to his daughter.
But Brady was quick to find the funny side of the occasion.
“Congrats on 14 years of college!!” Brady replied to Edelman’s tweet.
“That’s got to be another record you set!!”
In other Patriots news, the organisation has just signed free agent wide receiver Dontrelle Inman and offensive linesman Jared Veldheer.
Inman entered the NFL as a rookie free agent with the Jacksonville Jaguars in 2011 but was released at the end of training camp and then went to play in the Canadian Football League.
He came back to the NFL in 2014 with the San Diego Chargers and last season, he played for the Indianapolis Colts.
In his nine regular-season games he made four starts and caught 28 passes for 304 yards and three touchdowns. He also played in both Colts playoff games and registered eight receptions for 108 yards and a touchdown.
Veldheer is a nine-year NFL veteran.
He was a third-round draft pick by the Oakland Raiders in the 2010 NFL Draft, before going on to play for the Arizona Cardinals and last season for the Denver Broncos.
Veldheer has played in 118 regular-season games and has started in three postseason games.
He has started games at left tackle, right tackle and center during his career and last season with the Broncos he played in and started in 12 games at right tackle.