The comedy of errors that led to Palestinians' escape from Israel's Gilboa Prison
Israeli security officials said that the six men, who broke out of prison via a tunnel dug under a toilet in their cell, may have already made it to the occupied West Bank, Haaretz reported.
Some suggested that an escape to Israel might also be possible.
The detainees have now been in the free world for more than a day, evading desperate efforts by Israel's domestic intelligence agency and police force to catch them.
Early inquiries have indicated that a car collected at least some of the men three kilometres (1.86 miles) outside the jail.
Israel has established around 200 checkpoints to try to locate the detainees.
It was suggested on Monday that the six Palestinians could have travelled to their native Jenin city in the West Bank, The New Arab's Arabic-language sister service, Al-Araby Al-Jadeed, reported.
Their escape was facilitated by a series of errors made by the Israeli prison service.
Mobile phones are believed to have been involved in the breakout plot, and Omer Barlev, the Israeli public security minister, claimed the six probably worked with "outside assistance", The Times of Israel reported.
Despite technology having been brought in to block mobile phone coverage, prison authorities did not switch on this on or had it running at frequency too low to be effective, according to Israel's Channel 12.
At the time of their daring escape itself, the six Palestinians emerged from a hole beneath a watchtower, although the prison officer was allegedly sleeping at the time, according to Israeli reports.
Despite the police receiving a report about "three or so masked men" close to Gilboa Prison at 2:15am and then swiftly providing the jail this information, it took more than one hour for the facility to announce there were three escapees, and longer still to say there were six.
Back then, a passageway was burrowed below a bathroom located in the same jail, The Times of Israel said.
Three of the six men allegedly participated in a foiled prison break in 2014, not dissimilar to this week's, according to Israel's Walla outlet.
It is as yet unknown if the facility designs assisted the Palestinian detainees in their efforts.