Stoke agreed a deal for the US international winger last week, but he has not played since August following foot surgery.
Before finalising the deal, Stoke wanted to check on Shea but the MLS are fearful that he would not stand up to a rigorous medical.
His arrival in England has now been delayed as talks continue between all parties.
Another possible arrival that could be scuppered due injury is Dutch international Erik Pieters.
Stoke were due to watch the PSV Eindhoven defender on Friday - but because of cancelled flights their scouting party did not make the game.
That may have been a good thing, however, as Pieters was sent off against Zwolle, and on his way back to the changing room smashed part of the dugout which saw him suffer serious damage to his arm which is now set to sideline him for several weeks.