Gangs control around 80 percent of the Haitian capital, and violent crimes such as kidnappings for ransom, armed robbery and carjackings are common.
UN Secretary-General Antonio Guterres and Haitian Prime Minister Ariel Henry have for nearly a year sought international intervention to help support the police, but no country had stepped forward.
"Kenya has accepted to positively consider leading a Multi-National Force to Haiti," Kenya's Foreign Minister Alfred Mutua said in a statement late Saturday. "Kenya's commitment is to deploy a contingent of 1,000 police officers to help train and assist Haitian police restore normalcy in the country and protect strategic installations."
Its "proposed deployment" still required a mandate from the UN Security Council and approval from domestic authorities, he said.
"An Assessment Mission by a Task Team of the Kenya Police is scheduled within the next few weeks. This assessment will inform and guide the mandate and operational requirements of the Mission."
US Secretary of State Antony Blinken spoke by phone last night to Kenyan president William Ruto, according to State Department spokesperson Matthew Miller.
Kenya has participated in peacekeeping operations in its immediate region, including in the Democratic Republic of Congo and Somalia.
No other details about the Haiti deployment were immediately available.
Haiti, the Western Hemisphere's poorest nation, has seen compounding humanitarian, political and security crises, with gangs controlling most of Port-au-Prince.
Guterres said this month that violence had continued "to escalate and spread", citing murders, kidnappings, rape of women and girls, looting, and the displacement of thousands of people.
The UN chief, relaying a request from Henry, began calling in October for an international, non-UN deployment to help support police in the troubled nation.
The Security Council this month adopted a unanimous resolution encouraging member states "to provide security support to the Haitian National Police," including through "the deployment of a specialized force."
But the text, which was focused on a one-year extension of the mandate for the special UN political mission to Haiti, BINUH, stopped short of making any direct plans for such a force.
The council has asked Guterres to present by mid-August a report on all possible options, including a UN-led mission.
Earlier this month, Blinken said the US remained active in its search for a country to head a multinational force in Haiti.
This week, Washington ordered nonessential personnel and family of government employees to leave the country.
Staff at the US embassy in Port-au-Prince already live under tight security – confined to a protected residential area and forbidden to walk around the capital or use any public transport or taxis.