The 24-year-old joined the Magpies in a loan deal from Aston Villa until the end of the season on transfer deadline day.
The former Manchester City star has yet to make his Newcastle debut due to a knee problem.
“We thought it would be a couple of weeks,” Ireland told Newcastle’s official website.
“But I went running outside [on Thursday] at a decent level and decent pace, and I reckon it could be by the end of next week hopefully.
“I’ve just got to do a few more sessions and then see how far I can push it. If it goes well then I could be back soon.
“I haven’t got any specific game in mind. I’ve just got to take a day at a time really, because one day it could feel amazing and then the next day really bad.
“It’s quite strange, but I have to see how I feel on a day-to-day basis.”
“After two weeks at a club you want to be getting involved in the playing and training, but I’m not far away,” he added.
“I didn’t come here just to get treatment – I came here to play. Thankfully things are getting right now and I’m almost there.”