All three are expected to be fit for Thursday's Champions Trophy opener against Bangladesh at The Oval but Stokes' niggling knee problem is the biggest concern due to his value to the team.
"We're constantly monitoring him and trying to manage him as best as we can," England captain Eoin Morgan told British media ahead of the final match against South Africa at Lord's.
"We're trying to build it up again with the Champions Trophy in mind. It's a very strange injury, he aggravates it when he bowls, in his delivery stride. He's good to play as a batsman if need be but obviously we want Ben Stokes the all-rounder."
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Ali and Stokes put in respective Man of the Match performances in the first two matches against South Africa, while Woakes missed the second of them due to injury.
The June 1-18 Champions Trophy is being held in England and Wales and contested by the top eight sides in the one-day international rankings.
(Reporting by Aditi Prakash in Bengaluru)
