Indonesia’s TV One quoted an officer as saying the man who rented the house in question resembled Noordin.
It was earlier reported, though without official confirmation, that Noordin had been arrested.
Al Jazeera’s Steph Vaessen, reporting from Jakarta, said the gun battle was still going on after dark on Friday.
“Police are using spotlights on the house where four people are hiding. Local media is reporting that it is 80 per cent sure one of the men in there is Noordin Top but the police is still denying it.
“It is unclear if anyone has been hurt or killed.”
Noordin is one of two people suspected of being involved in the blasts at the Marriott and Ritz-Carlton hotels in the Indonesian capital last month.
Nine people were killed and more than 50 others injured in the blasts on July 17.
While Noordin has not been officially named as being behind the Jakarta bombings, officials and analysts have made clear he is the chief suspect.
Vaessen said: “It’s still not confirmed that he was actually connected to the latest bombings at the Marriott and Ritz-Carlton Hotel but … according to terror experts, there’s only one man in Indonesia who’s capable of doing it
Noordin was a key member of Jemaah Islamiyah (JI), an al-Qaeda-linked group that wants to establish an Islamic state across Southeast Asia.
But his group broke away from JI after an alleged falling-out with the leadership over the targeting of civilians.
JI is blamed, among other attacks, for the 2002 Bali nightclub bombing that killed 202 people.
Noordin is thought to have been behind attacks on the Jakarta Marriott in 2003 and the Australian embassy in 2004, and also on a series of restaurants in Bali in 2005 in which more than 20 people were killed.