Spurs have started the competition's group stages in fine form, beating Norwegian outfit Tromso 3-0 in their opening encounter.
Having reached the quarterfinals of last year's tournament, and indeed having won it with Porto in 2011, Villas-Boas is keen to go again, even though a place in the Premier League's top four is very much up for grabs.
"We had high expectations last season, we will continue with our expectations this season," he told UEFA's official website."It's a trophy that means a lot to Tottenham, last year we embraced the competition in a very serious way and we will continue to do so this season."
Spurs will meet an Anzhi side that has suffered a considerable downturn in fortunes in recent months, with Samuel Eto'o, Willian and Yuri Zhirkov, among several others, all leaving the club amid financial restrictions imposed by the club's hierarchy.
The Russian side is on a 13-game winless run and has not tasted victory in any competition since May, only managing a goalless draw with Moldovan club Sheriff in their first group game.
Tottenham is the bookies' favorite for the game at the Stadion Saturn, a 16,500-capacity stadium 1200 miles away from Anzhi's base in Dagestan, but it is set to be without a number of first-team players.
Midfielder Etienne Capoue and winger Aaron Lennon (both ankle) are definitely out, while Younes Kaboul (groin) and Danny Rose (ankle) are both doubtful.
Striker Emmanuel Adebayor has overcome an illness, but he is unlikely to be involved.
Ivorian forward Lacina Traore (shoulder) is Anzhi's most notable absentee, with Alexandru Epureanu (knee) and Ilya Maksimov also unavailable.
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