CalMac boss Martin Dorchester said that the Government-owned company is to consider the option later this year when new vessels are added to its fleet.
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 CalMac fleet.
Mr 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 "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 government service. It would have to pay for itself."
The chief executive also set out the ways in which Caledonian MacBrayne is modernising, with new hybrid electric-diesel ferries and making wi-fi available to passengers.
As yet, the departure point for any ferry into the city centre has not yet been decided.
A CalMac spokesman said: "We are continually looking for new 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."