The West Midlands side bolstered their striking options earlier this month by making Dynamo Kiev's Brown Ideye their new club-record signing.
Ideye adds to the likes of Victor Anichebe, Saido Berahino and Stephane Sessegnon who are available to Irvine in forward areas.
However, the Scot is planning to purchase another recognised striker before the start of his maiden season in charge at The Hawthorns.
"We've got Brown in now so that gives us three recognised strikers at the right level, and it would be lovely to have another one, but of course strikers cost a lot of money," Irvine told The Birmingham Mail.
"We have a budget to work to and rightly so, and it's a case of trying to stretch that as well as we possibly can.
"I would love us to be able to get in another striker because you want to have options of how you can play up front, but having said that I've been absolutely delighted with Victor Anichebe and Saido Berahino.
"I think they've been terrific since I came in, day in and day out in training."
West Brom open their Premier League season against Sunderland at home on August 16.