The presidents agreed to reschedule the summit, which Tunisia had been due to host, after two telephone calls between the leaders on Sunday, the official told Aljazeera's correspondent in the Yemeni capital.
Salih had called several Arab leaders and Arab League chief Amr Musa to discuss the need to hold the summit as soon as possible in the Egyptian capital, agencies quoted a Yemeni government source as saying.
But an Arab League spokesman in Tunis, Hisham Yusuf, said the situation was still in a state of flux and could not confirm the report from Sanaa.
"We have not been formally informed of a date," he told AFP, adding that "hundreds of calls" were being made between foreign ministers and the league's secretary general "on the steps to be taken in the next few days".
Arab countries have expressed regret and astonishment at Tunisia's decision late on Saturday to postpone the summit, which was due to open in Tunis on Monday.
The Cairo-based league accepted an offer from Egypt on Sunday to take over and host the summit - the first formal gathering of Arab heads of state since the US-led overthrow of Saddam Hussein last April.
In Cairo, sources close to Mubarak's office said several Arab leaders, including Saudi Crown Prince Abd Allah bin Abd al-Aziz and Jordan's King Abd Allah II, had approved "in principle" to the summit being held in Egypt's capital.
Syrian President Bashar al-Asad was also in agreement, along with the Yemeni leader, the sources said.
But Tunisia said it still wants to host the summit. The foreign ministry in Tunis insisted that Tunisia had the "right" to host the gathering because it currently held the rotating chairmanship of the 22-member Arab League.