Midfielder Mulumbu sat out Saturday's defeat against Crystal Palace due to an eye problem, while right-back Jones was ruled out after suffering concussion.
Striker Anichebe has been sidelined for the last five games due to a groin complaint, but all three are on course to be included in Keith Downing's squad.
Albion are set to be at full strength for the trip to St Mary's Stadium as Downing attempts to maintain his unbeaten record in the Premier League since taking interim charge following Steve Clarke's sacking last month.
Meanwhile, former Werder Bremen boss Thomas Schaaf has emerged as the latest favourite to take over as head coach at The Hawthorns.
The 52-year-old has been out of work since leaving Bremen by mutual consent last May after 14 years in charge of the Bundesliga club.
