Their 1979 peace treaty allows only a small presence of lightly armed Egyptian border guards in a demilitarised Sinai and also curbs Israeli deployment on its side of the frontier.
The Economist reported that Barak said Israel would also allow Egyptian helicopters and armoured vehicles into Sinai but no tanks other than one battalion already stationed there.
Officials in the Israeli defense ministry and prime minister's office declined comment on the report by the London-based weekly news magazine.
The killing last week of eight Israelis near the southern seaside resort of Eilat by militants whom Israel said infiltrated from the Gaza Strip via the Sinai stoked Israeli fears of Cairo losing its grip on the sprawling desert peninsula since the toppling of Hosni Mubarak in February.
With Israel's agreement to temporary reinforcements, Egypt had already beefed up its forces in the Sinai and had been waging an offensive against militants in the area before the cross-border assault.
Barak's latest reported comments appeared to go a step further, suggesting open-ended deployment.
An Egyptian intelligence official told Reuters that Israel had been more responsive recently to Cairo's demands for increasing its troops at the Sinai border, after rejecting such requests in the past.
"Following recent violence at the border, Israel has become more understanding of the security situation we are dealing with in Sinai," the official said speaking on condition of anonymity.
He added that Israel and Egypt have been holding discussions on altering security arrangements in Sinai and Egypt boosting the number of its troops there.
Five Egyptian security men were killed in clashes between Israeli troops and the gunmen, seven of whom were killed.
Israel has offered to conduct a joint investigation into the deaths of the Egyptians in the incident, which triggered anti-Israeli protests in Cairo.
In an interview with CNN on Thursday, Barak was cautious about the effect a bolstered Egyptian military presence would have on securing Sinai. "I am not very optimistic that it will all change in a matter of weeks," Barak said.