Spurs will host the Greek side in their fifth group-stage fixture of the Champions League campaign following a 4-0 victory over Red Star Belgrade in their last Uefa outing.
Jose Mourinho took over the reins of the north London side last week after the Lilywhites opted to part company with Mauricio Pochettino.
The Argentinian head coach led Spurs to their first-ever Champions League final last season before a 2-0 loss to Liverpool FC in the showpiece.
Spurs beat Borussia Dortmund, Manchester City and Ajax en route to the final in Madrid to underline their European pedigree.
Mourinho is a two-time Champions League winner with Porto and Inter Milan, having fallen short with Chelsea FC and Manchester United.
Former Arsenal midfielder Nicholas is backing Mourinho to guide Tottenham into the Champions League round of 16 thanks to a victory over Olympiakos.
“Olympiacos are bottom with a point and they got a cracking draw in the repeat fixture against Tottenham, who made it hard work for themselves with the thrashing from Bayern Munich,” Nicholas told Sky Sports.
“Jose Mourinho came in at the right time – Tottenham were down on their luck and feeling sorry for themselves, yet had bundles of quality. He should pick up the confidence easily.
“There are some problems still in defence. I think Serge Aurier is still rash, I am not sure how dedicated Danny Rose is to the cause, and I am unsure on the centre-backs.
“It will be a comfortable performance and three points, which means they will qualify. There are some favourable fixtures coming the way of Jose and after this one, he can say Tottenham are in the last 16 of the Champions League.”
Tottenham are unbeaten in their last five matches against Greek clubs since a 2-1 loss against PAOK in the 2011-12 Europa League group stage.
Spurs were 3-2 winners against West Ham United at the London Stadium in Mourinho’s first game in charge of the north London side.
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