The 21-year old USA international, who has attracted the interest of a number of English clubs recently, has been invited to the Emirates Stadium to trial with the Gunners which has been confirmed by his Major League Soccer club.
"The decision to send Shea to train with the Gunners was made after USA head coach Jurgen Klinsmann encouraged his MLS-based players to spend the off-season training overseas to enter January camp in top shape," an FC Dallas statement said.
Shea, who scored 11 goals in 32 appearances for the Texan outfit this season, has represented the US on seven occasions and is excited about getting his chance to train with a club such as Arsenal.
"To see how he [Wenger] does things ... he has had so many young players over the years and turned them into who they became, that experience will be pretty cool," Shea told Reuters.
"[Jurgen's] been pushing and wanting us to train in Europe in the off-season and it is good to get that experience.
"It's just strictly training, [getting] that experience and hopefully raising my game to another level.
"I think, obviously I am happy where I am, but I want to, eventually when the time is right, try it out and give it a shot."