The former Scotland and Rangers captain believes his Old Firm counterparts have what it takes to take a significant lead going into the second leg.
Both teams have had their share of the injury problems, however, Celtic are suffering far worse with a number of defensive injuries, while goalkeeper Craig Gordon and front man Leigh Griffiths are also sidelined.
Zenit, led by former Manchester City boss Roberto Mancini, will possibly be without Serbian veteran Branislav Ivanovic, whose fitness remains in the balance.
The fixture will see two old Premier League rivals in Rodgers and Mancini face up for the first time in a while, while Scott Sinclair, a former City man himself, will be out to prove to his former gaffer that perhaps he should have offered him more game time in their three years together at the Etihad.
Nevertheless, former Rangers captain and club legend Barry Ferguson has predicted a win for his former arch rivals. Zenit have scored 17 goals in the Europa League group stage this season and will be no pushover, with Emiliano Rigoni and Aleksandr Kokorin netting an impressive 11 between them to help the Russian side dominate Real Sociedad, Rosenborg and Vardar.
However, Ferguson believes that if the Hoops can keep it tight at the back at Celtic Park in the opening stages of the game without conceding, they have a real chance of going on to record a decent win.
Speaking to PLZ Soccer Ferguson said: "I think if Celtic shut up shop tonight, especially in the first 10 or 15 minutes, I can see Celtic winning by a couple of goals here.
"I don't think Zenit are a Champions League team, they're not a top, top team, and I think Celtic can defeat them tonight at Celtic Park.
"I think they'll win by a couple of goals tonight. They just need to make sure they close the door tonight and don't conceded any."
Celtic can take some confidence in the fact that Zenit are returning to competitive football for the first time since before their winter break.
Avoiding conceding will be a tricky task with an unsettled back four and Gordon's deputy Dorus de Vries between the sticks. However, should Rodgers' defensive unit hold it together, with a little help from Scott Brown, Celtic might just come good on Ferguson's prediction.