The former QPR and Dagenham and Redbridge stopper has been involved at the Gunners since 2008, stepping up from the youth team in 2011 to work with the senior goalkeepers.
Being an ex-Wales international it perhaps isn't a surprise that he is open to a move to Swansea, considering that they managed an excellent eighth place finish under Garry Monk last season.
Roberts' exit could be another indication that Chelsea goalkeeper Petr Cech is set to move to the Emirates, according to speculation in the Mirror. The Czech number one has long worked with Frenchman Christophe Lollichon and the exit of Roberts could leave an opening on the Arsenal coaching staff for another goalkeeper trainer.
However, Gunners legend David Seaman, arguably one of England's best ever goalkeepers, reacted with disbelief that his old club had let Roberts go, with the 45-year-old rated very highly by those associated with the game.
Going by what Seaman thinks, the Swans are about to receive a coach that makes Fabianski, one of the league's best goalkeepers last season, even better.