The Netherlands international missed Sunday’s 4-1 Premier League defeat to Manchester City and the midweek win over Liverpool with a groin injury.
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|3/10||United are 3/10 with Bet365 to beat West Brom this weekend.
"Robin will be back, involved somewhere. He trained today and is fit. But we'll have to see exactly where he is," he told reporters.
"Tom [Cleverley] has done a bit of training today. He rocked his knee in training and hopefully he won't be too far away."
Moyes admitted that he still had much to learn as United boss but once again took time to praise his players for bouncing back from Sunday's thrashing at the hands of their neighbours.
"I have been learning every week since the day I walked in. I don't think that's going to change for a long time," he added.
"We made seven or eight changes. We made sure everybody at Manchester United was able to show what they can do.
"The players showed they were hurt. We'll try to give the fans something to shout about again tomorrow."
United face a West Brom side that were knocked out of the Capital One Cup by Arsenal in midweek but Moyes is still expecting a tough test and is looking forward to meeting up with former Everton striker Victor Anichebe.
"Steve Clarke has done a great job. West Brom is a stable football club that has continued to progress," he said.
"I'm pleased he [Anichebe] got a good move. I hope he does well - but not against us."