The Baggies have signed eight new players so far this summer, including former Manchester City defender Joleon Lescott.
Irvine admits that the club is unlikely to bring in any new faces ahead of this weekend's trip to Southampton in the Premier League, though he is hopeful of boosting his squad before deadline day.
"I don't think anything will happen in the next couple of days, but there is a lot of work going on behind the scenes," the Scot told the Birmingham Mail.
"We are making enquiries and we're hoping something drops sooner rather than later. The chairman is certainly keen to do something before the deadline day."
West Brom opened their Premier League campaign last weekend with a 2-2 draw against Sunderland.