The Wales international stepped in for Foster in the club's 2-0 defeat to Swansea City in their last Premier League fixture.
Foster suffered a serious foot injury – expected to keep him out for another two months at least – in August and Myhill has the chance to step up.
But his position in the team is not guaranteed, with West Brom moving to sign goalkeeper Lee Camp on a free transfer before the transfer window shut.
"Obviously every club wants new players," Myhill told The Birmingham Mail.
"We as a group will always welcome good players. Of course, everybody wants to play every week. "It's not been possible for me. I hope the manager will show faith in me.
"I hope I can do myself justice [if I get the chance to play]."
The former Hull City man has made just 23 appearances for West Brom in all competitions since arriving in June 2010.