The airport and state government are at odds over whether the planned Tullamarine station should be underground or elevated.
The long-running stalemate has pushed back the project's completion at least four years until 2033 and forced the Commonwealth to appoint an independent mediator.
In 2018, the Victorian and federal governments committed to contributing $5 billion each to the project, expected to cost between $8 billion and $13 billion.
Melbourne Airport was part of a consortium the following year that offered up to $7 billion towards an underground airport station and express tracks from Sunshine to Southern Cross, but the offer was knocked back.
Despite suggesting the consortium's preferred route lacked additional stations, Mr Carroll signalled a willingness to restart formal discussions.
"If the offer still stands, we'll take the money please and let's get on and build it," he said on Monday.
"$7 billion in combination with the $10 billion from the Commonwealth and the state that makes it ... a $17 billion project. We'd be able to get it done tomorrow."
If the cheque was on the table, the deputy premier indicated the government would even be open to bending to the airport's demand for the station to be underground.
"Our preference is above ground but we can look at how they want to fully fund an underground (station)," he said.
However, Mr Carroll said the government could not let the airport "hold the state to ransom" and noted the potential problems from building underground.
"There is a massive amount of infrastructure that would need to be accounted for and expended on," he said.
"We can get this done if they stop being intransigent and stop protecting their car park revenue."
Rank-and-file Victorian Labor members passed a motion on May 19 to call on the state government to "get serious" about the rail link's development and for all parties to roll up their sleeves to get the project done.
In response, the airport said it remained supportive of a "future-proof" airport rail link and revealed it offered in April to explore potential funding opportunities.
The offer was reiterated to government following the May 7 state budget but its requests for a meeting were refused, the airport said.
AAP has contacted Melbourne Airport for a response to Mr Carroll's comments.