At the end of last month he was struck down by a hamstring injury just before half-time.
"I'm not too sure what the overall timescale on the injury is but it's coming along," Brunt told the WBA website.
"It wasn't as bad as we thought at first because it felt like a nasty one when I got it at Villa Park, so in that sense it isn't too serious.
"The problem is that it's happened a couple of times now so this time I want to make absolutely sure it's right before I come back, because it's no use to anybody doing two or three weeks at a time and then getting another injury.
"It is frustrating, but it's something you have to get used to in football."