The Premier League side had planned a 10am departure from Cardiff Airport but fog meant that was not possible.
A subsequent technical issue with the aeroplane Swansea had been due to leave on pushed back the departure time even further.
Club officials confirmed to Press Association Sport that the team were not expected to leave until 4.30pm at the earliest.
That meant it was unlikely they would train in St Gallen's stadium on the eve of the Group A match.
Manager Michael Laudrup was not with the squad, having travelled independently to Zurich, meaning he would be able to fulfil pre-match media obligations.
Swansea are well placed to qualify for the knock-out stage of the competition, standing second in their group, three points ahead of third-placed Kuban Krasnodar who face a difficult trip to Valencia.