Residents claim there has been four separate incidents in Parson Cross Park in the last few weeks in which a man has appeared and given chase to women. He has also been spotted trying to feed berries to children.
Officers from the Sheffield North East Local Policing Team have now stepped up patrols to provide reassurance to families in the area.
A South Yorkshire Police spokeswoman said: "There have been additional patrols in the area since the incident was reported to police but nobody has been identified and nobody has come forward with any further information or reports of suspected crime."
She added a number of concerns were raised about the situation on the LPT's Facebook page and the team would continue to monitor the situation.
In addition, residents described how he has been 'hiding in 5ft high long grass' and called for Sheffield Council to cut this back.
A spokeswoman for the authority said park rangers will visit to see if the greenery can be trimmed.
Francesca Allinson previously told how a man followed her while she was taking her daughter Imogen, aged two, to nursery one morning at the end of June.
The 22-year-old, who is also seven months' pregnant, told how she was now "too scared to go back into the park."
Another parent, Gemma Louise, told how she and her two children, aged two and four, were also followed by a man at about the same time.
Posting on Facebook, she described him as being "really tall, between 50 and 70-years-old with a shaven head and grey stubble."
Another concerned mum posted that a man was spotted "stood in bushes eating berries" and asked if her daughter wanted some of them. A neighbour moved the little girl away and he disappeared.
Gemma Voyse said a man jumped out at her while she was walking through the park and she was forced to run off from the scene.
Contact police on 101.