The proposal would see plush vessels using the King George V Dock in the Shieldhall District of Govan, the Scottish Daily Express reports.
The docks are located next to Braehead Shopping Centre on the boundary between Glasgow and Renfrewshire.
The plans were unveiled to Scottish Conservative leader Russell Findlay by Peel Ports after the politician recently visited the site.
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The West of Scotland MSP told the newspaper: “Seeing cruise ships coming up the Clyde into the centre of Glasgow would be a huge boost to Scotland’s biggest city and I’m delighted to give my party’s full support to this ambitious plan.
“If this happens, it has the potential to bring in huge numbers of visitors which would not only help benefit the economy but rejuvenate the riverside.
“Peel Ports have already overseen a massive increase in cruise ship visits to Greenock and are also investing huge sums in the advent of renewable energy.”
He added: “I would urge the Scottish Government and city council to encourage rather than stifle enterprising ideas like this.”
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The Tory MSP joined Councillor John Daly in discussions with officials from the port and Scottish Renewables.
John said: “I wholeheartedly support the plans from Peel Ports to bring cruise ships to the heart of the city.
“I am proud to represent this city and will always champion proposals like this which could deliver a much-needed jobs boost for Glasgow and help to give this area a much-needed shot in the arm.”
A spokesperson for Peel Ports told the Scottish Daily Express: “The potential for cruise ships to go further down the Clyde has been discussed in principle many times over the years.
“The Port of Greenock remains the Clyde’s cruise terminal, following the major investments into the facilities over recent years.”
