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Oliver Ford Davies, who played Polonius in the stage play, told The Daily Telegraph that production will take place in June.
Tennant, 37, sustained a bad back during the Novello Theatre run of the show, which meant that he only managed 11 performances at the venue.
The Dr Who star had already appeared in Stratford-upon-Avon, where some commentators described his performance as the best Hamlet of his generation.
Davies said: "We are intending to film it over two or three weeks in June. It won't be a full feature film as there isn't time but it will certainly be more than just the filming of the stage. It will be fantastic to work together again."
Ticket's for the RSC production sold out within three hours of becoming available last September.
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