Flinn is up for reelection this year, as are his colleagues on the council and Mayor A C Wharton. He said he is putting the proposal out there even though no one else is likely to support it before the election.
"People who think I wake up every morning worrying about reelection are wrong," said Flinn, half-joking that he would start a "Kamikaze Party" to propose unpopular budget options.
Memphis already has the highest combined city-county property tax rate in Tennessee. A 39-cent increase would amount to about 12 percent higher city taxes.
"Everybody knows taxes are going up and they're trying to get through this election year without doing it," he said.
The tax increase would be in addition to layoffs of some 200 city employees and other measures needed to balance the budget. Flinn said he talked to Wharton about his proposal and the mayor has "no philosophical differences with it as far as one approach."
The council meets Tuesday.