Mayor Joe Anderson clashed with members of his own Labour group last night over proposals that would see the council able to borrow up to £50m to invest in commercial property.
Former deputy mayor and rival Ann O'Byrne criticised proposals to set up a potential model for the fund that would allow money to be invested across the country.
The mayor has proposed potentially creating a fund of up to £50m that the council could invest.
The cash would come from within the city's current borrowing allowance.
Supporters of the idea say many councils across the country already have similar funds and that it can give struggling local authorities a vital source of money.
But the idea came under criticism from some councillors at last night's audit and governance select committee, with Councillor O'Byrne saying she felt the fact that the money could be invested outside of the Liverpool area meant it contributed little social value to the city .
She said: "I get it when we're investing in Liverpool.
"But we criticise our social landlords who are based in south east and buy property here.
"We slag them off all the time so I think we have to look at that if we are investing this money elsewhere.
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Mayor Anderson said that other forms of investment, such as the council's Invest to Earn model, did focus on the city region and that if the fund was set up it would provide money for services within the city, which faces immense budget challenges over the coming financial year.
He said: "If we don't have areas to invest in the city we will look at investing elsewhere. If there is money to be made, of course we will."
Mayor Anderson said that a large number of councils already invested along a similar model.
Liberal Democrat councillor Andrew Makinson also criticised the plans, saying it could be unwise to invest in commercial property now given the uncertainty over Brexit and Britain's retail industry.
