Swansea West MP Geraint Davies tabled the idea at a parliamentary inquiry about the promotion of Wales as a brand and destination.
The names of singers Sir Tom Jones and Katherine Jenkins were also suggested at the Welsh Affairs Select Committee meeting on Tuesday.
The airport said it kept its options constantly under review.
Mr Davies asked tourism experts to back his idea at Tuesday's meeting, saying: "The re-branding of [Liverpool] John Lennon Airport increased traffic 10-fold. Even [Doncaster Sheffield] Robin Hood Airport did well.
"I was wondering what you thought of the idea of renaming Cardiff Airport Dylan Thomas International Airport Cardiff?
"The idea would be to tag it with a global cultural brand that's got longevity, to tag Wales as a cultural destination rather than another part of 'England'," he said.
2014 marks the centenary of the birth of Dylan Thomas, whose works include Under Milk Wood. He died in 1953.
Hotelier Mike Morgan, who was giving evidence to the committee, suggested "Tom Jones Airport or Katherine Jenkins Airport".
Cardiff Airport has seen an increase in passengers since it was bought by the Welsh government in March 2013 for ??52m amid concerns about investment by its former owners.
Mr Morgan told MPs: "The airport is critical but I would stress that things are going in the right direction."
A spokeswoman for the airport said the issue of renaming it has been raised previously and that it always kept its options open to review.
Renaming Cardiff Airport after poet Dylan Thomas could improve Wales's international recognition, says an MP.