The France midfielder suffered a hamstring strain in last week's Europa League victory over Russian side FC Rostov and scans revealed he would be out for around three weeks.
The 24-year-old has been replaced by Monaco's Tiemoue Bakayoko in the France squad for the upcoming 2018 World Cup qualifier against Luxembourg and the friendly with Spain.
Pogba, however, was seen at Carrington over the weekend for treatment and a series of stretching exercises with United's medical staff.
The Red Devils now fully expect the player to be able to resume first-team training in a week's time, making him available to be selected for the visit of the Baggies to Old Trafford on April 1.
United boss Jose Mourinho has blamed the club's recent exhaustive fixture list as a contributory factor in the £89million man now being sidelined.
The 20-time English champions have been fighting on several fronts for silverware this season, having already clinched the Community Shield and League Cup, and they are still in with a shout of winning the Europa League.