Pogba has not played since limping off with a thigh injury on 6 February against Everton while van de Beek has missed his side’s last seven games – briefly returning to the bench during that run against Chelsea.
With Mata also unavailable, Solskjaer has had to rely on Scott McTominay, Fred and Nemanja Matic in central midfield with the manager’s options not improving ahead of the visit of high-flying West Ham.
United have three crucial fixtures before the international break which begins the last week of March – Sunday’s clash against the Hammers, the Europa League return leg against AC Milan and an FA Cup quarter-final away to Leicester City.
United have missed Pogba’s influence in midfield in recent weeks with the fixture against Brighton on April 3 now a possible return date.
‘No I don’t think any of those will be available [for West Ham],’ Solskjaer told a press conference.
‘We hope maybe before the International break. Maybe, but I’m not sure.
‘It is taking a little bit longer than we expected but we have three games now and then the international break and after that they will all be available for us.’
Marcus Rashford is also a doubt after picking up an ankle injury in last Sunday’s Manchester derby while Edinson Cavani could also miss out.