A deal worth around £3million is understood to have been finalized, and the player is due to arrive in England early next week.
Stoke want to put Shea through a couple of days of training to assess his fitness, as he has not played since August after undergoing foot surgery. But if Shea confirms his fitness, then Stoke will press ahead with a deal for the American international - rated as one of their finest prospects.
Shea had three goals and two assists in 21 games for FC Dallas before missing the final month with an abdominal strain stemming from the foot injury. He had 11 goals in 2011.
The 22-year-old has 15 caps with the U.S. national team, but missed two World Cup qualifiers with the injury. The final round of World Cup qualifying starts in February.
Shea returned to Jurgen Klinsmann's plans for the first time since a Feb. 29 exhibition at Italy. Shea was suspended for three Major League Soccer games for kicking the ball at an assistant referee during a game on May 17, then was benched for two games by Schellas Hyndman after arguing with the FC Dallas coach when he was taken out of a game on July 18. He also was part of the U.S. under-23 team that failed to qualify for the Olympics.
''I had good conversations the last week with Schellas Hyndman of FC Dallas and we both see a lot of upside in Brek Shea,'' US coach Klinsmann said during a conference call last year. ''We all knew that after the big disappointment of not qualifying for the Olympics that our youngsters from that program would eventually fall into a hole. They would go through emotional roller-coasters. That's what happened with Brek, he went through an emotional roller-coaster and he didn't have himself under control.''
''We think he needs our support and the feeling that we're there when things get tough,'' Klinsmann said. ''Brek has to learn to focus in and learn to become a full professional 24-7 and learn that the highest priority is what you deliver on the field and learn how to live off the field, and he's in the middle of that process.
"We coaches are responsible to help him in that process. We are happy to have him back and we'll have a couple good talks over a few coffees.''
The Associated Press was used in this report.