Both players have been out of action since West Brom's 3-2 League Cup win over Hull City last month.
Ideye picked up an ankle injury in the act of scoring his first goal for the club, while Anichebe has been hampered by a groin problem.
Anichebe's complaint appears to be the more severe of the two, although Irvine is hopeful that both will be able to return at the start of next week ahead of Manchester United's visit to The Hawthorns on October 20.
"We are expecting Victor and Brown to train at the beginning of next week - certainly Brown, Victor we are not as confident about," Irvine told West Brom's official website.
"He's 50-50 in terms of being able to train on Monday, but Brown we are almost certain will train then."
Winger Silvestre Varela should also be able to rejoin training after undergoing a minor operation on his groin.
