Allen, who has made seven appearances for the Potters this season, sustained a head injury during the first-half of Wales' 1-0 defeat to Republic of Ireland on Monday evening.
The Welsh midfielder is rated as a doubt for Saturday's trip to the Etihad Stadium, but Bowen is hopeful Allen will be available to take his place in the squad.
Speaking to the media on Tuesday, he said: "Joe is an early doubt,but we are still hopeful on him for the weekend although he did have to come off last night after suffering a bang to his head.
"We haven't seen him today because he only arrived back home late last night, and we wanted to give him the next 48 hours to make sure he is ready to come in on Thursday. We didn’t see any real need to get him in this morning, so fingers crossed he is ok and available for the game on Saturday."
Bowen added: "There is protocol to follow with injuries of this nature, which we will of course follow - the doctor will go around later today to see him, but he will come back in on Thursday and we will assess him then."