With the club under new Chinese ownership, he is also keen to keep England Under-21 striker Saido Berahino, who Stoke City have made an offer for.
"We are looking to bring five players in if we can," Pulis told a news conference.
"I'm more confident things might drop this week than I was last week.
"Nobody is more keen for Saido to stay than me. He is forming a good partnership with Salomon Rondon."
Rondon scored the winning goal as Albion began their Premier league campaign with a 1-0 win at Crystal Palace last weekend.
They play at home to Everton on Saturday.
Stoke manager Mark Hughes confirmed on Friday that his club were interested in signing Berahino.
"It is in the public domain that we have made bids," he told reporters.
"They have had a change in ownership and we haven't moved forward since then. They are looking to improve their group too so maybe their attentions are elsewhere."