Rangers have to get past Gibraltar side St Joseph's or Prishtina of Kosovo in the first round, while Cork will face the winners of the preliminary round match between Progres Niederkorn of Luxembourg and Welsh representatives Cardiff Metropolitan University.
But, should both clubs progress, they will meet in the next round - and the Irish side are keen to stage the home leg at the 7,485-capacity stadium.
Club chairman Declan Carey told the Irish Examiner: "We have the category licence to play our second round game in Turner’s Cross.
"Unless we’re told otherwise by [the FAI and UEFA], our plans are to stay in Turner’s Cross and play our European games there as much as we can.
“Obviously plans can change but Turner’s Cross is our home ground and that’s where we feel we’ll perform our best in Europe.”
One factor that could impact on the decision to hold the game at Turner's Cross is the 1984 UEFA Cup game between Bohemians and Rangers. Bohs recorded a memorable 3-2 victory but the occasion was marred by crowd trouble at Dalymount Park and the streets of Dublin.
Nearly 15 years later, security concerns prompted another Dublin side, Shelbourne, to forfeit home advantage in a UEFA Cup tie with the Light Blues, instead playing the game at the neutral venue of Tranmere Rovers' Prenton Park.
Asked about a similar move from Cork, Carey joked: "There would be security concerns, because I know there’s lots of Liverpool fans in Cork who will probably want to get a selfie with Steven Gerrard.”
However, the chairman fully believes the Rebel Army would meet all the logistical and security demands that come with such a high-profile match.
“With every tie we assess all of the security measures that are required. We plan efficiently and effectively, we’re professionals and we treat every game or potential tie with the seriousness it deserves.
“We’ve played big teams before that have brought large crowds to Turner’s Cross, like Genk and Legia Warsaw and Rosenborg, and I’m sure it would be a packed out crowd at Turner’s Cross for Rangers if that game does come to fruition.”
Officials from both clubs held informal talks in Nyon yesterday after the draw, with the Scottish Premiership side understood to be concerned that the capacity of Turner's Cross would only allowe for around 400 away tickets for a side with close to 50,000 season ticket holders.