The Swans' goalless draw against Malmo in Sweden ensured a 4-0 aggregate win in their third qualifying round tie, andmeans they will be seeded when the draw for the next stage of the competition is made later today.
Although never threatening to find the fluidity shown during the first leg, a Swansea side showing seven changes were rarely troubled at Swedbank Stadion.
Indeed they could have enjoyed another comfortable win had Michu, Wayne Routledge and Jonathan de Guzman not failed to make the most of their best opportunities, while record signing Wilfried Bony had a goal incorrectly chalked off for offside.
Another clean sheet also means Swansea have conceded just one goal in their build-up to their Barclays Premier League opener against the reigning champions.
Laudrup believes his side are in good shape.
"We are ready, not only for United but in general," the Dane said.
"Part of that is from winning this round and not conceding, and also a lot of our players have got a full 90 minutes under their belts.
"Last year it was completely different, because we had two friendlies last year the week before the season started.
"So we are ready. That does not mean we will win against United, but we are ready."