The Hoops will hope to make home advantage count ahead of what is sure to be a tough test in next week's return leg in Russia.
The Scottish champions, however, have failed to win any of their last five Europa League ties on home turf and bet365 offer 8/5 (3.60) that Brendan Rodgers' men buck the trend here.
bet365 also go 12/5 (3.40) that the match remains level after the first leg.
Patrick Roberts, Leigh Griffiths, Tom Rogic and Craig Gordon are all sidelined for the Hoops.
Emiliano Rigoni and Aleksandr Kokorin scored 11 goals between them in the group stage for the Russians and will pose a live threat to the Scottish champions.
Zenit scored 17 group stage goals - more than any other team in the competition - while there have been goals at both ends in 11 of Celtic's last 12 matches in this competition.
The Hoops have conceded at least two goals in each of their last five Europa League ties at Celtic Park.
Tips and predictions
There is plenty of potential for the goals to flow in this game and bet365's 4/5 (1.80) quote for at least three goals to be scored could represent excellent value for punters ahead of Thursday's tussle.
Odds correct at time of writing. Please gamble responsibly.