The midfielder suffered an achilles tendon injury in training last week and missed the Carlisle game on Saturday. He looks set to miss another two weeks of action, as does Jason Price who has a similar injury, but Taylor is confident that fringe players at the club can step in and do the job.
He said: "We're not sure when Ashbee and Price will be back, although I'd say that at the moment they are both doubtful for next week. You've got to be careful with those kind of injuries.
"However, there are no plans to go out and bring in anyone else. We've already got enough quality in the building to cope."
Winger Ryan France should be back in action for the home match with Torquay on Saturday, while there's also the option of starting Jon Walters. Stuart Green would move back to his usual central midfield position.
Partnering him could be either Damien Delaney or Richard Hinds, who were both chosen to play in midfield at Carlisle under criticism from many fans. That decision has been defended by Taylor though.
The City boss said: "I had to make changes against Carlisle because of the injuries. I thought it was going to be hard and I wanted some strength in midfield so that's why I picked the team I did. If we were playing Carlisle next Saturday, I'd do the same thing."