A permanent tribute to the 60 infants whose remains were lost by Emstrey Crematorium has been in the planning since Shropshire Council agreed to fund the memorial in 2017.
It was initially proposed to be sited in the Dingle flower garden in Shrewsbury's Quarry Park.
However, Shropshire Council is now consulting on it instead being placed within the cloister garden at Longden Road Cemetery.
The new location was suggested by the town council at a meeting involving the two authorities and Glen and Louise Perkins, who never received the ashes of their four-month-old daughter Olivia and later set up campaign group Action For Ashes.
Shrewsbury town clerk Helen Ball said: "Originally we were asked whether it could go in the Dingle, and we were cautious that the Dingle isn't a remembrance garden.
"I was asked to go to a meeting with Shropshire Council and Mr and Mrs Perkins, and we had a discussion about the memorial.
"The design is lovely, but I expressed concerns to them and the council that it is not really the place for such a memorial.
"I had concerns that we could not give them the peace and quiet and space for reflection that they rightfully want.
"So we suggested the cloister garden might be a more appropriate place.
"It is part of the old chapel, it is a really nice area, there is parking on site and it is probably open longer hours than the Dingle.
"I explained we could look at changing the planting to make it more sensory."
The change of location comes after the design of the memorial was also changed when the initial design, by stone carver Lottie O'Leary, was rejected by the families. The new version depicts a baby within a dandelion being cradled by a hand.
Shropshire Council is now asking parents whose children are to be remembered by the memorial for their views on the change of site.
The consultation says: "All parties involved with the memorial are very keen to ensure the memorial is provided as soon as possible for all parents.
"Understandably, because of the range of views parents have and the number of parents being consulted with, we recognise it may be a challenge to provide a memorial and in a location that every parent agrees with unanimously.
"We recognise too, the emotional strain this process is putting upon parents, taking this into account there is a desire to proceed with the memorial as soon as possible. If a unanimous view cannot be achieved it may be necessary to proceed with a majority view."