Instead the Senegal striker will be lining up for opponents West Ham on Saturday and looking to improve on his tally of three goals in five games.
Stoke had agreed a ?7.1million fee with Hoffenheim only for the move to break down over concerns about Ba's previous knee injury.
Coates told the Sentinel: "There are no qualms about the decision we made. We would have taken the player had he passed the medical.
"But we were strongly advised by our medical team that it was a risk we could not take. You cannot spend large sums of money on a high-risk basis.
"We were disappointed, though, because we wanted to sign the player and the eventual decision was nothing to do with is ability."
Source: PA
Source: PA