The Swiss side are unbeaten in four games at St Jakob-Park and have not conceded a goal since their second group game against Genk.
Basel saw off Dnipro Dnipropetrovsk in the last 32, a result of which club president Bernhard Heusler was very proud.
He told Basler Zeitung: "For the first time for many years, we have eliminated a top club in the knockout phase. This is another milestone in the club's history."
Zenit, the only other reigning domestic champions left in the competition, will present an even bigger challenge, with the 2007/08 UEFA Cup winners among the big spenders in Europe.
They splashed out 40million euros on striker Hulk in September and Heusler knows how much Dnipro would have loved to go up against their neighbours.
He said: "An encounter against Zenit would have been the greatest thing for Dnipro. That our young team has defied this strong team, there can be a cruel pride."
While a clash between Dnipro and Zenit would have had more of an edge to it, Basel would probably have preferred to play Liverpool, who were knocked out on away goals by the Russians in the last 16.
Heusler admitted Basel lost money on the tie against Dnipro, but he said: "I think it makes no difference in terms of audience. It's knockout football. At some point, people have to decide whether to come for FC Basel or on account of the opponent."
Zenit will be favourites to progress but they may need to rely on their performance in the home leg.
Luciano Spalletti's side have won only once in 10 European away games and have failed to score in five of those matches, while they have not made it past the last 16 since winning the title.
Recent signing Luis Neto made his Europa League debut in the home leg against Liverpool, and was particularly impressed with the atmosphere at the Petrovsky Stadium.
He told Zenit TV: "The stadium was full. It was a good atmosphere, the fans were enthusiastic. They always push for the team, they're always singing, and it's a good experience playing at the Petrovsky."