The 42-year-old, who left Southampton to take over at White Hart Lane in May, got his tenure off to a winning start on Saturday as close-season signing Eric Dier's stoppage-time goal gave Spurs a 1-0 victory at West Ham on the opening day of the Premier League season.
Pochettino will be looking for his side to build on that victory on Thursday with a positive result in the first leg of the final play-off round, with the return encounter set to take place in London seven days later.
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Lewis Holtby, Andros Townsend and Michael Dawson, who were on the bench at Upton Park alongside Soldado and Davies, may also figure.
Last season, Spurs made it through the group stages of the competition but were eliminated by eventual runners-up Benfica in the last 16.
AEL, who missed out on a seventh Cypriot top-flight title last term when they lost on the final day against rivals APOEL, have already recorded an impressive 1-0 victory over Zenit in the third qualifying round of this season's Champions League.
A 3-0 defeat in the second leg of that tie meant that they dropped down into the Europa League and set up the clash with Spurs and their coach, Ivaylo Petev, knows that the odds are heavily stacked against his players progressing further in the competition.
He told Uefa's official website: "They are a massive club and it is crucial we minimise our mistakes against them because they know how to punish every little error.
"The truth is that this was a very difficult draw for us and we were not so lucky. It is very important that we are ready for the first game and play well."
Thursday's match will not be the first time these two sides have met, with Tottenham having played a series of friendlies – one of which was against AEL – during a visit to Cyprus in 1968. Spurs were 7-1 victors in that game, with Alan Gilzean scoring a hat-trick, Cliff Jones netting twice and Jimmy Robertson and Dennis Bind grabbing the other goals.