Ronnie Coleman, aged 13, vanished on Friday afternoon after attending a family funeral at City Road cemetery and a wake in Darnall.
His mum, Tina Dell, 45, from Arbourthorne, issued a plea for him to return home yesterday - stressing that the youngster was not in trouble.
Today, detectives searching for Ronnie said there are not believed to be 'any 'suspicious circumstances' surrounding the disappearance and warned that anyone offering him a place to stay faces prosecution.
Superintendent Bob Chapman said: “As the days pass, our concern for Ronnie’s welfare grows.
"It is now six days since Ronnie was last seen or heard from, which is incredibly worrying in any missing person investigation, but especially because he is a child.
“Ronnie is 13 and while we don’t think there are suspicious circumstances surrounding his disappearance, we also have no information to suggest that he is safe and well so we have to consider that he could be at risk of harm.
“Our absolute priority is ensuring Ronnie’s wellbeing and if we find out that anyone has been offering him a place to stay and obstructing the police and public’s efforts to find him, those individuals could be in trouble, with consideration given to potential child abduction offences.
“I’d therefore stress again that anyone with information about Ronnie’s whereabouts comes forward to police and tells us what they know. Your information will be treated in strict confidence. Please help us find Ronnie safe and well.
“The support from the public so far has been great and we know many of you have offered to help search areas of Sheffield for Ronnie."
He said a sighting of Ronnie on the Manor estate yesterday is being followed up.
Call South Yorkshire Police on 101.