Tickets went on sale at 10:00 am on Wednesday, but many fans camped out overnight to make sure they didn't miss out as Roma prepare for their first semi-final in this competition since Liverpool beat them on penalties in the final to lift the 1984 European Cup.
"Many will spend the night awake, standing in line, all hoping to give themselves a place in the history of their favourite team," one fan tweeted.
"I've got three generations of Roma fans at home and I hope we can gain our revenge in this game," 85-year-old Vincenzo Ricci, who queued through the night, told Roma News.
Ticket prices for the May 2 match at Rome's Stadio Olimpico range from €60 (AU$95) to €160 (AUD$255).
Italian airline Alitalia announced it will schedule special flights to bring Roma fans to Liverpool for the first leg in Anfield next Tuesday, returning to Rome the following day.