Veteran Phillips has been nursing a thigh injury he sustained during the Blues' pre-season friendly against Real Mallorca, leaving him frustrated on the sidelines.
But the 37-year-old is nearing a return to full fitness and could be in contention to take on the Baggies at the Hawthorns on 18 September.
Phillips says the weekend clash against Liverpool will come too soon for him, however he hopes a week of training will give boss McLeish a selection headache.
Phillips told the Birmingham Mail: "The injury is fine. I'm not getting any more pain or symptoms.
"It's just now trying to catch up on fitness, trying to tick all the boxes with the medical staff.
"We're not far away. I'd say if you're going to ask me when I will be ready, Liverpool on Sunday is probably a bit too soon.
"I will need at least a week's training with the lads. So I'm hoping to be involved in some capacity in the West Brom game."
Phillips arrived at St Andrews in 2008 to help City back into the Premier League, and he has since gone on to net his 250th career goal in a blue shirt.
McLeish offered the front man a year contract extension over the summer to keep him on the Midlanders' books until next summer.
Phillips says he will still be playing by that time, insisting his age hadn't hindered his fitness.
The former Sunderland man doesn't know whether he'll be offered an extension by the club, however he is certain he will still be plying his trade - dismissing suggestions he would hang up his boots.
"I will definitely still be playing, I'm sure of it," added Phillips.
"Whether it's still at Birmingham, who knows. But retirement, no, I haven't thought about that at all.
"I have still got plenty to offer. At the moment this has probably made me more hungry now, sitting out for a month.
"It is doing my head in. I can't wait to get back training. I feel I haven't started. I am nearly ready and raring to go, hopefully the club will see a benefit from that."