Midfield duo Youssouf Mulumbu (groin) and Paul Scharner (Achilles) and striker Shane Long (back) have all been back in training ahead of the match against the Canaries.
The Baggies are also hopeful that defender Jonas Olsson will overcome a calf injury in time to feature, while Jerome Thomas is recovering well from a groin problem.
With the club "optimistic" Gareth McAuley, who came off in the second half of the FA Cup win over Cardiff last time out, will shake off a calf injury, manager Roy Hodgson looks set to have plenty of options to choose from.
"Jonas hasn't trained yet but we're hopeful for Saturday," West Brom assistant head coach Keith Downing told the club's official website.
"We'll have a little look today (Wednesday) and when the boys get together again tomorrow we're hopeful he might train then.
"There are one or two who trained yesterday and one or two who didn't.
"We're waiting to see how Scharner reacts after training yesterday and we're hopeful for Saturday on him.
"Thomas hasn't trained but again we're looking for him to maybe go in tomorrow, similar to Jonas.
"There is a good chance he'll make it and Mulumbu is the same.
"He trained over the last couple of days, the reaction yesterday was okay and we're optimistic about him.
"Long trained a little bit yesterday, not the full training session, and he's being dipped in and out this week, so we're pretty hopeful on him.
"McAuley didn't train on Monday but really improved in his rehab yesterday so we're optimistic about him as well."
Zoltan Gera (knee) and Chris Brunt, who fractured his right ankle in the New Year's Day defeat to Everton, remain long-term absentees for West Brom, though there is some good news over the fitness of Steven Reid.
The former Republic of Ireland international has been struggling with knee and ankle problems but is still on course to be back by the end of January.
Downing added: "Reidy had a good day yesterday but with long-term injuries you can have good days and bad days.
"He's still on course for returning in around a month."
