The city has been shortlisted alongside Coventry, Paisley, Stoke-on-Trent and Sunderland - a bid by St Davids, Pembrokeshire, failed to make the cut.
A team behind the Swansea bid previously said it planned to match the £33m spent by Hull if it wins the cultural title.
The City of Culture for 2021 will be announced in December.
It is the second time Swansea has been shortlisted for the title, the city lost out to Hull in the competition for the 2017 award.
The team behind the 2021 bid had previously said it wanted to host a programme of events which play on the "'lovely, ugly' Swansea that Dylan Thomas describes."
It now has until the end of September to submit a final bid before the winner of the third City of Culture is awarded by the UK government.
Welsh Secretary Alun Cairns said while there would be disappointment in St Davids, he hoped the people of Swansea would get behind the race for the title.
"Boasting the UK's first area of outstanding natural beauty, and the region that brought the first passenger railway to the world, Swansea's amazing achievements, past and present make it a true contender to be crowned UK City of Culture 2021," he said.
"I know that they will put forward the strongest case possible in the race for the title and I hope that local people take every opportunity to get behind the bid."
If successful the city, which is set for a £500m regeneration, would host a series of cultural events, including festivals, art and theatre performances, following in the footsteps of Derry/Londonderry and 2017 title-holder Hull.
It would also have access to a £3m Heritage Lottery Grant.
Swansea is in the running to become the UK's City of Culture for 2021.