The international force is aimed at tackling rampant gang violence in the Caribbean nation, which killed nearly 5,000 people last year, and is due to be initially financed by the United States.
The mission was thrown into doubt after the Kenyan court ruled that it would be unconstitutional to deploy officers abroad unless there was a "reciprocal arrangement" in place with the host government.
Ruto said Haiti had asked for help months ago, and he expected a request would come shortly that would satisfy the demands of the court.
"So that mission can go ahead as soon as next week, if all the paperwork is done between Kenya and Haiti on the bilateral route that has been suggested by the court," Ruto said following an Italian-Africa summit in Rome.
Asked if discussions were underway with Haiti to get the necessary request, Ruto said: "Absolutely. Haiti have actually written formally, not today, several months ago."
Haiti first sought help in 2022 as gang violence surged but was unable to find anyone willing to take charge, with many foreign governments wary of supporting the impoverished country's unelected administration.
Kenya, which has a long history of taking part in international peace-keeping operations, stepped forward last July and committed 1,000 police officers, saying it was doing so in solidarity with a brother nation.
The Bahamas, Antigua and Barbuda, and Jamaica subsequently said they were willing to help, with the United States pledging $200 million to get the deployment off the ground.
"The mission is on course. The mission is a bigger calling to humanity," Ruto said, stressing that it was a police rather than a military operation.
The United Nations said last week that it had documented 4,789 people killed by gang violence in Haiti last year, an increase of 119% from 2022, and that another 3,000 people had been kidnapped.