The Robert Burns International Federation told the public petitions committee the name change would attract fans from across the world.
The group has attracted 7,000 supporters for a Facebook campaign to re-title the struggling Ayrshire airport.
The Scottish Government took over Prestwick last November to avert its closure and Ayrshire-born Deputy First Minister and infrastructure secretary Nicola Sturgeon revealed last month she was “not unmoved” by calls for the name change.
Federation chief executive Alison Tait said: “Robert Burns is a global icon, recognised worldwide”.
She said naming the airport after the poet “would immediately identify its geographical location right in the heart of Burns country, almost in sight of Burns’ birthplace.
“It would be a fitting and relevant tribute to the memory of Robert Burns.”
Ms Tait said the new name would give south west Scotland the opportunity to capitalise on its golfing and ancestral research attractions.
She said there was potential for capitalising on the Burns connection throughout the airport, with Burns already worth £160 million to the Scottish economy.
Ms Tait said this could help boost passenger numbers, which plunged from a peak of 2.4 million in 2007 to 1.1m last year.
It could also boost jobs in the area, which has above-average unemployment.
Federation senior vice-president Jim Thomson told the committee visitors would immediately recognise the airport’s location if it had Burns’ name, while many were unfamiliar Prestwick.
The campaign follows the lead of other airport name changes involving famous locals, such as John Lennon in Liverpool, Robin Hood in Nottingham and George Best in Belfast.
Wick Airport has changed its name to John O’Groats.
Committee chairman David Stewart described the petition as “very good” but said it would await recommendations from the Scottish Government’s advisor on Prestwick’s future strategy.
The airport’s controversial “Pure Dead Brilliant” branding has already been removed.