Arriving passengers would be whisked up the Clyde into the city centre in 25 minutes.
Boats would operate from a pontoon on the White Cart Water about 500m east of the airport.
The plans include passengers transferring from the terminal in golf buggy-style vehicles.
These would eventually be replaced by a travellator – a moving walkway – which would have to go either over or under Abbotsinch Road.
The scheme has been devised by John Hillis, who runs power boat trips on the Clyde in Glasgow.
He reckons the route would provide visitors with a stunning introduction to the city.
Hillis also said more transport options to the airport were required as it continued to grow, It handled more than 1 million passengers for the first time in June and the annual total has grown by 7 per cent, to 9.7m.
Hillis, director of Pacific Quay Powerboats, said: “There are already plans for a tram-train link, and with the existing M8, the river is an obvious third option.”
He is undeterred that river taxis were considered “impractical for access to the airport” in a 2012 study on improving access to the terminal, which led to the plans for trams which can also run on rail lines.
Hillis said: “The views and the experience will make it the best way to arrive in Glasgow, passing landmarks such as the Glasgow Science Centre, the Armadillo and Finnieston Crane.
“It is the classic scene shown on those postcards of the city – with audio commentary along the way.”
He hopes to initially operate two ten-seat covered vessels to provide a half-hour frequency service.
The water taxis would cruise at 25 knots (29mph)with a top speed of 30 knots (35mph).
Hillis said: “It’s not going to be as quick as taking the bus but it will be more enjoyable.”
He hopes to emulate the service provided by the classic wooden motorboats – or vaporetti – transporting passengers from Venice Marco Polo Airport.
Hillis said: “Our waterways are as much a part of the city as Venice’s are, it’s just that we do not use them – they are perceived as being a bit grotty.”
A spokesman for Glasgow Airport said: “We meet regularly with a number of transport operators to discuss links to and from the airport.
“We met with Pacific Quay Powerboats as part of our ongoing engagement with transport partners.”