The proposals, on a site in Gresley Road, are set to be approved by members of Sheffield Council's city centre, south and east planning board at a meeting on Tuesday next week.
The new one-storey children's centre would be built next to a youth centre and community hall, and would involve building over a car park and basketball court.
However, if the scheme goes ahead, a new hard-standing games area to replace the court would be built in nearby Greenhill Park.
Objectors who have signed the petition organised by the Greenhill and Bradway Tenants and Residents Association say that they support the children's centre in principle, but object to the location.
They have claimed an entrance direct on to Gresley Road is not appropriate, additional cars using the centre would cause traffic congestion and the removal of the court "will be felt within the community".
Planning officers have recommended the scheme go ahead.
The officials have claimed the proposed centre, which would have 64 part-time places for children, would form an "important community facility" in Lowedges, where there is currently a shortage due to the rising birth rate.
Funding for a new children's centre has to be spent before March next year and this is the only possible site after building at Lowedges Primary School was ruled out.
Officials said: "Overall, it is considered that the proposed centre would provide significant benefit to the local community in terms of extra educational services, at a particularly important phase of a child's development.
"On balance it is therefore considered that the reduction in the range of options available to the youth club is outweighed by the benefits to the community which would arise from the proposed children's centre."