The Baggies have made just two signings so far this summer, bringing in Jay Rodriguez on a £12m deal from Southampton and completing the loan capture of Egyptian centre-back Ahmed Hegazy from Al Ahly.
The Midlands outfit have been linked with a string of names in recent weeks, however, including Middlesbrough's in-demand defender Ben Gibson, Barcelona centre-half Thomas Vermaelen, Everton midfielder Gareth Barry and Crystal Palace defender Joel Ward.
"We've got five targets," Pulis told reporters yesterday. "I'm excited at the opportunity of trying to get some of these players in.
"We know what we're after and we are desperate to bring them in, but must be patient."
West Brom, who finished 10th in the Premier League last season, begin the new season at home to Bournemouth this afternoon.