Condoleezza Rice, the US secretary of state, made an unannounced visit to Beirut on Monday where she called for UN action on the disputed Shebaa Farms.
Israel captured the area from Syria in 1967 and it is now claimed by Lebanon as part of its territory.
Israel fought two wars in Lebanon and occupied an enclave in southern Lebanon for 18 years until 2000.
In the summer of 2006, Israel fought a 34-day war with the Lebanese Shia group Hezbollah, which last month reached an agreement with the ruling coalition to form a national unity government.
Israel recently announced that it had resumed indirect talks with Syria, eight years after negotiations were suspended.
On Wednesday Israel reached a ceasefire deal with the Palestinian Hamas group.
Regev's comments on dialogue with Beirut came as the Reuters news agency quoted a Lebanese political source as saying that Hezbollah and Israel were close to reaching a prisoner-exchange deal.
The deal, mediated by a UN-appointed German negotiator, would see Hezbollah returning two Israeli soldiers captured in 2006 for four Lebanese prisoners and the bodies of about 10 Hezbollah fighters, the source was reported as saying.
It is not clear whether either of the Israelis is still alive.
Hezbollah fighters captured them in a cross-border attack in July 2006, prompting a 34-day conflict.
Earlier this month, Israel released a man who had served a six-year jail term on charges of spying for Hezbollah.
On the same day, a Hezbollah official announced that the group had released what they said were the remains of Israeli soldiers killed in the 2006 war.