It follows an appeal yesterday in which police stressed there could be an innocent explanation for the man going up to the lone child.
The girl and her mother had been walking near to Armley Primary School in Salisbury Terrace when they became separated at around 8.30am on Monday.
School staff joined the girl's mother in searching the area and found her being brought back to school by her grandmother.
The girl had returned to the family home, which is around half a mile away from Salisbury Terrace.
She said that a white man with brown hair had approached her during the time she had been missing.
Acting Det Insp Amanda Wimbles, of Leeds District Safeguarding Unit, yesterday said: “We are still in the process of getting details from the young girl involved and we are carrying out enquiries to clarify the circumstances around the male approaching her.
“We would like to hear from anyone who saw this five-year-old girl walking either alone or with this male between the school and the area around Stanningley Road at any point between 8.30am and 8.55am when she was found.
“We appreciate there may be an innocent explanation around the involvement of the male and we would also ask for that person to contact us so that we can resolve this matter.”
A police spokesman today said that officers were continuing to work with the girl to build up a better understanding of the circumstances.
Anyone with information is asked to contact Leeds District Safeguarding Unit via 101 quoting reference number 13180142279.