Romano Prodi, the Italian prime minister, said on Monday that he had informed Kofi Annan, the UN secretary-general, that Italy was willing to lead the mission.
"I confirmed the Italian willingness. He [Annan] will decide about the command," Prodi said, adding Annan would make his decision by this weekend.
"He will do that after completing all of the analyses and meetings with all of the leaders of all of the countries that could be interested in the mission," Prodi said.
France had wanted to lead the proposed 15,000 strong force despite only offering to contribute 200 non-combat troops.
Arturo Parisi, the Italian defence minister, has also said that his German counterpart, Franz Josef Jung, had said that Germany favoured letting Italy head the mission.
Parisi, in a statement, added that Germany promised a "significant participation" in the UN mission, but did not elaborate.
Lebanon earlier on Monday said that Beirut had accepted an Italian offer to contribute 2,000 troops to the force, the most substantial commitment yet.
The Italian government has approved sending up to 3,000 troops.
In contrast, France, the country initially expected to lead the force, has scaled down its commitment to 200 extra troops, citing worries about the chain of command.
Italy's centre-right opposition, mindful of the public sensitivity to military casualties, said Rome's enthusiasm was unmatched by its neighbours.
"Chirac will send a few generals, Germany a launch or two, while we have to send troops dressed as kamikazes in the Italian flag," said Francesco Storace of the rightist National Alliance.