The council funds add to the £37,000 already raised by the Hillsborough Justice Campaign (HJC), but with the total cost of the structure amounting to £152,000 further donations are being sought.
Mayor Joe Anderson has now called for the city's two clubs to contribute and appealed for public help in identifying a home for the statue.
Mr Anderson told reporters: "We will find somewhere prominent in the city for this monument.
"I'm open to suggestions from the public as to where that might be. It seems right to me it should be sited in the St George's Hall quarter.
"I think it is right the memorial is away from the ground as the disaster affected everyone no matter what club they are affiliated to.
"I was at the second semi-final at Villa Park where Everton were playing, but I could so easily have been at Hillsborough if the venues were different.
"I hope the two clubs make a similar contribution to this monument and others will rally behind it."
Sheila Coleman of the HJC revealed the monument will display the words "Hillsborough Disaster - we will remember them", and will include two plaques with the names of the victims engraved.
Family members of the victims will also be invited to add objects to a sealed inside section, whilst the public will be encouraged to contribute letters or poems for the box.
"What we are trying to do is make it inclusive, something that is by the fans, for the fans," she said.
Merseyside artist Mr Murphy's other creations include the statue of John Lennon at Liverpool John Lennon Airport, and the sculpture of Billy Fury outside the Piermaster's House in the Albert Dock.