The estimated cost of the Sydney gateway project connecting the WestConnex tollroad to the city's airport and port has more than doubled to as much as $1.8 billion, a leaked document shows.

The blowout of up to $1 billion in the expected cost of the motorway link to the airport, from $800 million, threatens to push the total bill for WestConnex to $17.8 billion.

Details of the escalation are contained in a Transport for NSW document obtained by Labor. It estimates the cost of the gateway at between $1 billion and $1.8 billion, and shows that the project has received a "health check" from Infrastructure NSW.

The gateway was one of the original justifications for WestConnex but there remain few substantial details on its likely final shape years after the government committed to the controversial motorway.