The 29-year-old aggravated the injury once again in the warm-up before Sunday's 2-0 victory over Southampton at The Hawthorns, but managed to play through the pain.
"Ben is in Germany [to see a specialist]," Sky Sports News quotes the Scot as saying. "Most of you noticed on Monday night that he was kicking with his right foot and not his left foot.
"He has gone out to see a specialist. We are waiting on the diagnosis. Fingers crossed, it is positive and I'm hopeful he is available to play again at the weekend, kicking with his right foot.
"It is a problem with the groin and hopefully it is something we can manage in the same way as with Shane Long and his hamstring over the last few weeks. If we can manage him, then we can get a few more games out of him. What are his chances for Saturday? Probably 60-40 in his favour."
Foster has been first choice with the Midlands outfit since joining from Birmingham City before the start of last season.