The firm's chief executive Martin Dorchester said that the Government-owned company is to consider the option later this year when new vessels are added to its fleet.
CalMac Ferries' service many Scottish islands and it has recently put two routes on three-year trials, between Ardrossan in Ayrshire and Campbeltown in Kintyre, and between Mallaig in Lochaber and Lochboisdale on South Uist.
But running a river bus on the Clyde would be a new venture, which Dorchester stressed would have to pay its own way.
As yet, the departure point for the ferry into the city centre has not yet been decided. A decision on where it would berth in Glasgow has not been decided either.
The river ferry would be brought in when spare capacity becomes available after this summer, with three new ferries due to be added to the Caledonian MacBrayne fleet.
Dorchester said: "There are many opportunities around our network. The fact that the contract CalMac runs is called Clyde and Hebridean ferry services gives a clue about where we want to develop things, so there's an opportunity there."
He said a river bus service "could come right into the city. Our view is to maximise the Clyde as much as we can".
He added: "We wouldn't see that as a subsidised overnment service. It would have to pay for itself."
Speaking in an interview with the Sunday Herald yesterday, Dorchester also talked about the special circumstances of being a state-owned public service, as well as a business, and of preparing a competitive bid for a new licence.
That process starts this year, and the new licence is expected to begin in 2016. CalMac lost its bid to continue running the mainland ferry link for Orkney and Shetland, losing 30% of its business.
The chief executive has also set out the ways in which Caledonian MacBrayne is modernising, with new hybrid electric-diesel ferries; looking to smart ticketing with rail and bus services; working with other tourism operators; offering more day trip and flexible tickets; and making wi-fi available to passengers.
The firm is also providing more locally produced food and drink onboard its ferries.
Plans for the Clyde river bus remain very much on the drawing board, however.
Previous plans to run river buses from Rothesay and Greenock by private firms have failed to get past the planning stage, and it remains to be seen if CalMac's scheme will take to the water.
The CalMac spokesman said: "As an ambitious award-winning ferry operator we are continually looking for new commercial opportunities and a ferry service on the Clyde in Glasgow is something which is suggested from time to time.
"We will potentially have vessels available as a result of new ships coming into the fleet so it makes sense to see how they might be used in the future.
"It is too soon to say what shape or form the service would take, or indeed if it would be viable, but it is something we would like to investigate."