Burnley are believed to have had two bids for the defender rejected, with reports suggesting that the most recent offer of £1.5m was not enough to encourage the Baggies to begin negotiations, and Irvine is hopeful that there will be no more interest in the 24-year-old.
"My first signing after I came in was Joleon Lescott - that was so we could have four centre-backs that I feel comfortable with, and right now we have four centre-backs I am comfortable with," the Scot is quoted as saying by the Birmingham Mail.
"I'm not wanting to lose any of those centre-backs. Craig is on the way up. He's played for England Under-21s, he's 24 years old and he's not a player we want to lose.
"I think he will stay with us. He's going with us to the States and it'll take a very good bid for anyone to make the club accept it."
Irvine reportedly rejected a transfer request from Dawson earlier this summer.