The Journey will be filmed in Northern Ireland in the autumn, and follows Mr McGuinness's developing friendship with the late First Minister Ian Paisley.
English actor Timothy Spall is set to star opposite Mr Meaney as Dr Paisley.
The film is being written by County Down-born novelist and screenwriter Colin Bateman.
Sources close to the production have told the BBC that discussions with Mr Meaney are at an advanced stage and agreement should be reached shortly.
The plot of the film centres on a fictional journey Mr Paisley and Mr McGuinness take together that leads them to forge a friendship.
Dublin-born Mr Meaney is one of the Republic of Ireland's best-known and most versatile actors.
He played Chief Miles O'Brien in the TV series Star Trek: The Next Generation and Star Trek: Deep Space Nine for more than a decade, becoming one of the show's most prominent characters.
And he has also appeared in a number of hit films including The Commitments, Con Air, The Damned United and Alan Partridge: Alpha Papa.
He has also had an extensive career on stage and TV, appearing in a number of shows and productions.
Mr Meaney supported Mr McGuinness in his bid to become president of Ireland in 2011, and spoke at a rally in Dublin's Mansion House alongside the Sinn FÃ©in MLA.
There had previously been speculation that Liam Neeson and Sir Kenneth Branagh were being lined up to play the former first minister and current deputy first minister of Northern Ireland.
The producers and director of The Journey are Mark Huffam, Piers Tempest and Nick Hamm.
They were the team behind the 2011 film Killing Bono, which was also filmed in Northern Ireland.
Irish actor Colm Meaney is in "advanced talks" to star as Deputy First Minister Martin McGuinness in a new film.