The Scottish champions, who are seeded, could land an enticing tie against Barcelona, but the Kazakhstani side SSHVSM Kairat are also in the second pot. They play in Almaty, which is even further east in Asia than Astana, where Celtic lost to Shakhter Karagandy last month.
"I'm trying not to even think about it," admitted Carol Anne Stewart, the City chairwoman. "If we were drawn against them it could have a huge impact on our finances."
Unlike Celtic, who had a £12m pot of gold waiting for them after beating Shakhter over the two legs, a trip to Kazakhstan would have no reward for City other than the prospect of reaching the last 16.
The Glasgow side normally budget on spending £6000 to travel to a last-32 away leg, but the cost would be considerably higher to get to Almaty. It would also be a logistical nightmare for the amateur club.
The trip would also require visas for the players and extra time off work. Ironically, had City not been seeded for the first time they couldn't have met Kairat.
For footballing reasons, the Scots will also want to avoid No.17 seeds Tyreso. The Swedish club boast Brazilian star Marta in their ranks and two of the 10 players nominated for the inaugural Uefa best women's player in Europe award, which will also be announced today.
Tyreso apart, being among the top seeds gives City an excellent chance of reaching the last 16 for the second time in three seasons. A tie against Barcelona, who lost to Arsenal in last season's competition, would be challenging but would almost guarantee a sell-out crowd at Petershill Park for Eddie Wolecki Black's side.
Arsenal and Birmingham City are also in today's draw as first seeds, as are holders Wolfsburg.