Alli, who has not started a Premier League game since early September, is expected to return to training next week following a hamstring problem.
However, Saturday's game at West Ham and next Wednesday's trip to the Netherlands will come too soon for the England international.
Rose withdrew from the England squad last week after suffering a groin strain in the final minutes of Spurs' 1-0 win over Cardiff, and he is expected to be sidelined for a further week.
Spurs must beat PSV to have a chance of reaching the Champions League knockouts after losing their opening two group games to Inter Milan and Barcelona.
Pochettino will, however, have Mousa Dembele, Serge Aurier and Christian Eriksen available at London Stadium after muscle injuries, while Jan Vertonghen remains sidelined with a long-term hamstring problem.
However, Mousa Dembele and Christian Eriksen are available for the London Stadium after thigh and abdomen injuries, respectively.
"[The international break] was a good time for us because we are going to recover a few players like Christian and Mousa Dembele," he said. "Still maybe 10 days more for Dele Alli and Danny Rose is the same – one week more.
"Jan Vertonghen is a little bit longer. But the most important thing is that we start to recover players. It will be a tough month of competition for us.
"There are a lot of games ahead and it’s so important to have nearly all the squad fit to compete and play and to give options to rotate and share the games because it will be tough, the months we have ahead.
"We have seven games in one month, in four weeks, and it’s so important to have all fit to compete and to give the level that we want."
Spurs face Manchester City in 11 days' time, leaving both players with a chance of facing the champions.