Other issues are likely to include the lifting of an Israeli air and sea blockade of Lebanon, policing of the Lebanese-Syrian border to stop arms-smuggling and a possible prisoner swap between Israel and Hezbollah.
Annan, the UN secretary-general, is due to meet Fuad Siniora, the prime minister, and Nabih Berri, the speaker of the Lebanese parliament on Monday. He is seeking the full implementation of UN Security Council resolution 1701, a UN spokesman said at the weekend.
The resolution ended a 34-day war between Israel and Hezbollah on August 14. It also made a series of demands on Israel, Lebanon and other countries which have yet to be met.
It urged the reopening of Lebanon's airports and harbours, blocked by Israel since the start of the war, and the securing of Lebanon's land borders.
The resolution called for UN members to provide enough troops to allow it to boost the size of its current Unifil force in Lebanon from 2,000 to 15,000.
Annan discussed the European Union contribution to the expanded force with leaders in Brussels on Friday.
He said France, which has promised 2,000 troops, would lead it until February when Italy, which has pledged 3,000, would take over.
"We should deploy, I hope, within the next few days, not the next few weeks," Annan said after the talks.
The UN hopes to boost the size of
peacekeeping forces in Lebanon
A close aide to Siniora said Annan would brief the prime minister on the Brussels talks.
"But the government will press him first to pressure Israel to end its blockade on Lebanon because it violates Security Council resolution 1701 and threatens stability in Lebanon," the aide said.
Israel says until the expanded Unifil force arrives to police southern Lebanon, the blockade is essential to prevent weapons reaching Hezbollah.
Since the end of the war has continued to control commercial planes flying in and out of Beirut demanding that they go through Amman, Jordan.
Israel wants UN troops to police the 375km Lebanese-Syrian border, but Syria has said such a move would be hostile and has threatened to close the border if it happens.
That would effectively cut Lebanon off from the outside world as the country's only other land border is with Israel, with which it has no diplomatic ties.
Nasrallah says there may be talks
on negotiations over prisoners
Resolution 1701 does not call for the deployment of UN troops to the Lebanese-Syrian border but asks Unifil to assist the Lebanese government "at its request" in securing the country's borders.
Also expected to be discussed is the release of Israeli and Hezbollah prisoners, including two Israeli soldiers whose capture by the group on July 12 sparked the war.
Hezbollah wants to exchange them for some of the thousands of Arab prisoners, including Lebanese, in Israeli jails.
Annan has said both sides will have to make "painful compromises" to get what they want.
As well as visiting Beirut, Annan is expected to travel to southern Lebanon. He will go to Israel on Tuesday and is also due to visit Syria and Iran as part of his Middle East tour.
While the fragile truce was holding on Israel's northern border, there was no end in sight for violence in the Palestinian territories where an Israeli air strike killed four members of the Hamas-led security force during ongoing clashes in the northern Gaza Strip on Monday, medics and witnesses said.