The former Celtic manager, known for winning trophies in his second season at clubs, faces pressure to bring success in the competition.
Spurs are 1-0 down as they head into the second leg of their Round of 16 tie against AZ Alkmaar.
Former manager Tim Sherwood is optimistic that Spurs will not only progress but go on to win the entire tournament.
Mr Sherwood told Foot Italia: "If Spurs win the Europa League, there’ll be a statue of Ange Postecoglou outside the club.
"I say that because he would’ve delivered on his mandate of winning a trophy – and they’ll qualify for the Champions League for next season in the process."
He believes that winning the Europa League would not only be a triumph on the field but a significant boost off the field.
Mr Sherwood added: "It would also be a massive win for the club off the pitch, on the recruitment side of things.
"Players looking for a new club will warm to Spurs in the transfer window if they’re offered Champions League football."
He praised Spurs' facilities and the prospect of playing under an attack-minded manager, but warned that success in the Europa League is crucial.
Mr Sherwood continued: "However, for that all to happen, they must win this competition.
"I think they will win it; I have a sneaky feeling that they’ll go and lift the trophy.
"If they don’t, it could be a very difficult few months for everyone involved at Spurs.
"It will be a very hostile environment at the club if they come away empty-handed this season."