The Potters announced after the 2-2 home Premier League draw with Wigan on Tuesday night that they had reached an agreement over FC Dallas player Shea, whose switch from the Major League Soccer outfit is subject to him passing a medical and obtaining a work permit.
The 22-year-old was a spectator at the game and following it, Stoke manager Tony Pulis - less than a week after he had appeared to indicate that a deal for Shea would not be happening - was quoted on the club's official website as saying: "I think it is close now, and we are hoping that we can get that deal done in the next day or so.
"Brek is a very, very exciting player, and one who we believe could go on to become a very good player for the football club."
In his post-match press conference, Pulis also confirmed he had received an inquiry from his QPR counterpart Harry Redknapp about Stoke striker Crouch.
Redknapp has admitted his interest in recruiting Crouch, who he has managed before and was an R's player earlier in his career.
Pulis said the situation was ongoing but emphasised both that Crouch was "very happy" with the Potters and that any deals Stoke are involved in have to be right for the club if they are to go ahead.
"Harry has rung me up and asked me about the possibility," Pulis said. "I have spoken to Peter about it and then it is up to Peter whether he wants to go. Peter is very happy here and he has made that clear.
"The important thing for me is that if he does want to go, it has to be right for us and also we have to make sure we have someone who will come in and do the same job.
"To do all that over two days is going to be ever so difficult."