Police say the arrested men e-mailed photos of Pearl
Mr Pearl, a 38-year-old correspondent for the Wall Street Journal, vanished two weeks ago in Karachi, where he was trying to trace Taleban or al-Qaeda leaders who may have fled Afghanistan.
Police say the link to Sheikh Omar came after arresting three men in the city of Karachi who are alleged to have sent e-mails containing photographs of Mr Pearl in captivity.
"It's a major breakthrough for us and we are confident that we will be able to reach Pearl soon," the police official told Reuters.
India regards Mr Omar as one of its most wanted criminals.
He was freed from prison in India in 1999 as part of a deal to secure the release of hostages on a hijacked Indian Airlines plane.
Another man freed in the deal was Maulana Azhar Masood who went on to found the extremist group, Jaish-e-Mohammad.
The group has been banned by both the US State Department and the Pakistan Government for alleged terrorist activities.
"There is a connection to Jaish in Pearl's kidnapping," Pakistani police told Reuters.
However, Jaish-e-Mohammad appeared to distance themselves from the kidnapping on Wednesday.
A spokesman told the BBC that Sheikh Omar had never been a member of the group.
Wife's appeal
Mr Pearl's pregnant wife, Mariane, has renewed her calls for his release in an interview with Pakistan's The Nation newspaper.
"By holding Danny they are preventing a man from writing about their concerns and accomplishing his chief work," she said.
Mr Pearl was trying "to create a bridge between cultures so we can start finding true solutions to the conflicts that are causing so much suffering in the world," she told the paper.
Arrests
The three men arrested in Karachi are said to have told police that they were not involved in the kidnapping.
They say they were given the photographs by someone else with instructions to send them, and do not know the current whereabouts of Mr Pearl.
A previously unknown group calling itself the National Movement for the Restoration of Pakistani Sovereignty said in the e-mails that it was behind the kidnapping.
They set two deadlines which have now passed, threatening to kill him if their demands were not met.
Police have named three other people they want to talk to - Hashim Qadir, Mohammad Bashir and Imtiaz Siddiqui, who is said to have telephoned Mr Pearl twice.
Police say they may have been involved in putting Mr Pearl in contact with the leader of an Islamic group he was on his way to meet when he disappeared.
Pakistani authorities are determined to find Mr Pearl before President Pervez Musharraf visits the United States next week.
Wall Street Journal managing editor Paul Steiger has written another open letter to the kidnappers, pleading for them to make contact again.