"Evidence we're getting leads us to believe that he is the man", said one officer, who declined to be identified because he was not authorized to disclose investigation details.
The Catholic Church in Pakistan has strongly criticized police and officials for failing to make any arrests over the rape and murder of seven-year-old Zainab Ansari.
Sources said Umar's polygraph test has been taken but the report has not been received yet.
On January 16, a Supreme Court bench expressed displeasure over the lack of progress by the Punjab government and police on the case of Zainab's rape and murder. The suspect has been handed over to the Kasur police who are now going to conduct a DNA analysis. During the proceedings, Punjab additional inspector general (AIG) and advocate general (AG) informed the court about the progress made in connection with the case. "What has been done in the case so far?" the chief justice had enquired.
A police official, who is part of the joint investigation team (JIT), requesting anonymity, said the suspect had targeted the children of the families with the strong social background which triggered public outcry, Dawn reported.
Sharif did not confirm the arrest in his remarks to media after the meeting, but said the police and other law enforcement agencies were close to solving the case, promising a breakthrough would come very soon. Every case is handled in the same manner which allows culprits to win their freedom due to incomplete investigations, he had added.
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The place where Zainab's body was found is surrounded by buildings on the busiest road of Kasur - Shahbaz Khan Road.
Her body was later found in a rubbish dump, triggering a nationwide outcry against the crime.
According to the initial post-mortem report, the minor was strangled to death after being raped multiple times.
Moreover, the authorities have informed that the suspect's mobile phone location shows he was in Kasur.
Earlier, District Police Officer Zahid Ali Marwat had said that the abuse and killing of minors were widespread in other districts of Punjab as well, but the incidents in Kasur overshadowed all other districts.