Teixeira is struggling with a fractured toe, while Mulumbu was close to making his Baggies debut against Fulham last Sunday before suffering a thigh strain.
Mowbray is hoping Teixeira will be fit to face Everton, although the former Hibs boss believes Mulumbu will be out of action for up to two weeks.
"Whether Filipe trains on Thursday, we'll have to wait and see," he told the club's official website. "The main injury he's got at the moment is a fractured toe.
Frustrating"It's frustrating for [Mulumbu]. He trained very well during our four days away in Spain. For no apparent reason, he felt a thigh problem in training on Friday.
"He pulled up, which was a blow to him and potentially to us, because he might have had a part to play at Fulham. Hopefully, it is just a few strained fibres and not a tear because it was very innocuous.
"Maybe it's just caught up with him a little bit after a week or two. Hopefully, it's not too bad, although I would suggest he probably won't be ready for Saturday or Tuesday."
Meanwhile, Mowbray believes this weekend's clash against Everton will come too soon for injured duo Jonathan Greening and Jonas Olsson.
Little chance"I don't think either Jonno or Jonas have got a chance for the weekend," he continued. "They're both coming on really well.
"Jonathan might join in some light training on Thursday but, for me, there is no chance of us throwing him in. Jonno's not far away but I would suggest he needs some training first.
"I think we've got to make sure Jonno doesn't come back too early and then ends up missing another six weeks because the season would be virtually over then.
"In an ideal world, we need to get him back and then keep him back for the rest of the season."