Honda's Chief Executive Takanobu Ito is set to make an official announcement as early as Thursday, one of the sources added.
The Japanese automaker quit the sport at the end of 2008, handing over their team to then-principal Ross Brawn who went on to win both titles in 2009 with Mercedes-powered Brawn GP.
One source said Honda hoped Formula One's new engine regulations for 2014 would help develop technology for its mass volume road cars, adding: "That incubator aspect of the sport makes Honda's participation worthwhile."
Formula One is set to introduce a new 1.6 litre V6 engine next year aided by high-power turbo technology with energy recovery systems.
The news about Honda's return to Formula One was reported earlier on Wednesday in Japanese media including public broadcaster NHK and Asahi newspaper.
"There is nothing we can say at the moment," Honda spokesman Shigeki Endo said.
McLaren are committed to using engines made by Mercedes, their former shareholders, next year but have not revealed their plans for beyond that date. A team spokesman had no comment on the reports.
The link-up with McLaren, the second most successful team in the sport after Ferrari in terms of race wins and drivers' titles, would revive one of the greatest Formula One partnerships.
Honda had little success with their own team but powered McLaren to multiple championships with the late Brazilian triple champion Ayrton Senna and French four times champion Alain Prost between 1988 and 1992.
The partnership in 1988 was the most dominant in Formula One history, with Senna and Prost winning 15 of the 16 races.
The sources said Honda also hoped renewed participation in the sport will help boost vehicle sales, especially in Japan, Asia and Europe where Formula One is popular.
The two sources declined to be named as they were not authorised to speak about the matter.
Honda made its Formula One debut at the 1964 German Grand Prix at the Nuerburgring. The company's first grand prix win came just a year later at the 1965 Mexican Grand Prix in Mexico City and they then withdrew after the 1968 season.
They returned to the sport as an engine provider in 1983 and departed again in 1992.
In 2000, Honda made a comeback with BAR, which then became the Honda team in 2006. The only success in that period was Jenson Button's 2006 win in Hungary.
Button, world champion in 2009, is now a McLaren driver along with Mexican Sergio Perez.
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