Losing the former Chelsea star would be a blow to the Russian club as it appears Celtic may not be the only team without their full defensive contingent.
The former Chelsea stalwart picked up an injury a few weeks ago but his recovery has not gone as expected, with the Serbian expecting to have been given the go-ahead this close to the game.
The 33-year-old three-time Premier League champion still has a chance of playing if a last minute scan suggests he is fit. However, the veteran's inclusion in the squad to travel to Glasgow has been put in jeopardy.
Zenit are coming off the back of their winter-break but have been playing warm-up fixtures to re-gain some match fitness going into the knock-out tie.
Their last game came against Maribor which ended 3-1, however, Ivanovic was not given permission to play by the club doctors.
According to the Sun, Zenit boss Roberto Mancini said: "He must undergo a physical examination. He must meet with a doctor and then we can say when the period of recovery will finally end. All we can do is rejoice at the fact that we do not have other serious injuries."
Perhaps Zenit should genuinely rejoice in the fact that they do not have any other serious injuries.
Ivanovic is no doubt an important player to the Russian giants, however, their list of injured players is dwarfed by that of Celtic.
With Craig Gordon and Leigh Griffiths sidelined for sometime, the Celt's defensive injury problems, which appeared to have lightened, were exacerbated when both Dedryk Boyata and Kristoffer Ajer limped off in a recent loss against Kilmarnock.
Ajer has since returned to partner Jozo Simunovic at the heart of defence, yet the lack of continuity in terms of back four selection has been severely detrimental to Celtic's results this season and is not what they need going into their biggest game of the season.