Dundalk, who now lead the League of Ireland, were the team with lowest coefficient rating in the draw and will play their home leg at the 51,700-seater Aviva Stadium in Dublin, rather than at the 4,500-capacity Oriel Park.
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The draw for the Champions League Group stage will take place on 24 August with the first round of matches to take place on 14 and 15 September.
Dundalk, the surprise team in qualifying, will play Legia Warsaw, and Hapoel Beer-Sheva is away first against Celtic.
Last season’s semi-finalists came fourth in the Premier League last season but are now managed by Pep Guardola and will have designs on winning the trophy.
City’s potential opponents in the draw are either Roma, Monaco, Young Boys, Rostov or Steaua Bucharest.
A seeded champions route team such as Tom Rogic’s Celtic could face one of the unseeded champions route teams such as Dinamo Zagreb, Ludogorets Razgrad, FC Copenhagen, Hapoel Beer-Sheva and Dundalk.
The tie of the round will see Porto meet Roma.
The first leg will take place on 16th/17th August, with the return leg taking place on 23rd/24th August.
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Even if City do avoid Roma they could face Monaco, who finished third in Ligue 1 last season, or the 3,800-mile round trip to Russian club Rostov in amongst the start to their Premier League campaign.
