Steve Clarke hopes there is still room for ‘one, maybe two’ more arrivals before the new season begins.
Albion are on the lookout for a left-sided defender and a striker, not least as Simon Cox is expected to leave the club.
The Baggies have already signed Ben Foster and Claudio Yacob on permanent deals, with Yassine El Ghanassy arriving on loan from Belgian club Gent.
They have been linked with Arouna Koné, of Levante, although reports claiming Albion had made an offer for him are incorrect.
Koné is expected to go for a big fee this summer, despite only having one year left on his current deal.
That could inevitably price Albion out of the market should they try to pursue him.
Although there is still a month of the transfer window to go, Albion would ideally like new players in before the new campaign kicks off in mid-August.
Clarke wants players who will challenge for first-team places.
“There’s room for one more player, maybe two,” he said.
“We’re looking all the time. We won’t do anything unless we can bring someone in to improve the squad.”
The Albion boss has been pleased with what he has seen of his players so far.
“We have three weeks, three more games,” he said. “We need to use that time well but we are progressing along the right lines.
“The 3-0 scoreline in Copenhagen flattered us but it was nice to win. It’s good for confidence. It was good to get a second clean sheet on Saturday. That’s a solid foundation.”