Alli was injured when Spurs beat Fulham on January 20, but his return has not come in time for him to be included in Pochettino’s plans for Tuesday’s Champions League game against Borussia Dortmund.
The manager hopes to have the England midfielder back in his squad when Tottenham face Southampton in the Premier League on Saturday, with Spurs now only four points ahead of fifth-placed Arsenal following three games without a win.
Speaking ahead of Tuesday's tie in Germany against the Bundesliga leaders, Pochettino said: "I think Dele is close, we will see if it is possible for him to be involved on Saturday against Southampton."
Spurs will also be without full-back Kieran Trippier when they take on Dortmund, leading as they do 3-0 on aggregate following the first leg at Wembley three weeks ago.
Trippier has featured in Spurs' last two games – the 2-0 loss to Chelsea at Stamford Bridge when his own goal condemned his side to defeat – and Saturday’s 1-1 draw against north London rivals Arsenal.
Pochettino said: "Kieran Trippier is at home after two games. He was so tired, and has a small problem."
Harry Winks and Eric Dier have both travelled, however, and will be in the matchday squad, but the Argentine is doubtful whether either player will be fit to play from the start.
"We need to assess both,” he said.
"They are here because we need one day more to assess. Dier is a lot of time to not play. We will see if he can be on the bench - I don't believe he can start. Winks is the same."
Should Tottenham make it past Lucien Favre’s side and into the last eight, it will mark their first quarter-final appearance in Europe’s premier competition since 2011.
Spurs were thrashed 4-0 in the Bernabeu before losing out 1-0 at White Hart Lane to a Cristiano Ronaldo goal.