The Nigerian striker took a knock soon after scoring his first goal for the club in the League Cup victory over Hull City last week.
Ideye missed West Brom's 4-0 win over Burnley last Saturday, but head coach Alan Irvine expects the 25-year-old to be back soon - possibly in time for their visit to Anfield.
"Brown didn't train yesterday but he is making progress, he is improving," Irvine told the club's official website.
"I am hoping he has a shout for Liverpool. He has rocked his ankle, it isn't too bad.
"These things come down to your pain tolerance levels. There are some players you can strap up and will be okay, there are some who take a little bit longer.
"Nobody can see how much pain he's feeling and I am certainly not playing down what he has got it the way of injury - but it isn't something serious.
"He hasn't badly damaged his ligaments, he hasn't broken his ankle, there's nothing major going on there. He has rocked his ankle - as he scored the goal their defender landed on his standing foot."
Irvine expects to be without Victor Anichebe and Silvestre Varela at Liverpool due to groin problems, but Chris Baird is in contention after recovering from illness.
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