The former Bond girl has been involved in early workshops for the production from a script by One Man, Two Guvnors writer Richard Bean.
It is understood Arterton would be in line to play the lead role of Rita, played in the film by Sally Hawkins.
Producers Stage Entertainment told the BBC they would "very much love her to be part of the production".
It has not yet been announced which London theatre the musical will be staged at, but it is hoped it will play next year.
"As with all casting there are schedules to work out, but we'd very much love [Arterton] to be part of the production when it opens in the West End," a spokesman said.
Early workshops were directed by Rupert Goold - the new artistic director of London's Almeida Theatre - with the score written by David Arnold, who also provided the music for the Bafta-nominated film.
Made in Dagenham told the story of the machinists who went on strike in 1968 at the Ford Dagenham car factory demanding equal pay and protesting against sexual discrimination.
The character of Rita played a pivotal role in leading the strike and meeting former employment secretary Barbara Castle, leading to the Equal Pay Act 1970.
The film also starred Andrea Riseborough, Jaime Winstone and Bob Hoskins.
Gemma Arterton is set to star in a West End musical version of the 2010 film Made in Dagenham.