The issue was discussed at an online meeting of the parish council last month.
Councillor Jenni Errington, chairman said: "We have received correspondence requesting a litter bin for Quarry Bank we will ask city councillors to consider."
Allison Riddell, parish clerk, asked councillors which of the town's bins should be relocated.
She added that she would speak to the city council over councillor's suggestions.
Councillor Martin Spears said: "Well, I have had a quick look round and there is three on Irthing Park that go right down to the fire station,there is three on Gelt Road.
"There is three within 10 metres of each other so I' sure that we can rearrange them in a better location if need be."