The 28-year-old actress has portrayed Clara Oswald, assistant to the Eleventh (Matt Smith) and later, Twelfth (Peter Capaldi) Doctor, on the BBC series since 2012. Coleman is expected to leave the role in the program's annual Christmas special.
"The conversations about Jenna's exit have started and a plan is in place which is being ironed out," a source told The Mirror. "By the time she leaves she will be one of the longest-standing companions ever. She has been absolutely brilliant in the role, but everyone agrees it is a part that should change after a period."
"It was very much a mutual decision," the insider added. "It's important to keep the series moving and fast-paced, and the time is just starting to feel right and the feeling is that it could be a perfect Christmas storyline."
Actress Rose Leslie, who portrayed Ygritte on Game of Thrones, has been suggested as a replacement companion by some fans. Ygritte was killed off in season four of the HBO series, and Leslie will appear in ITV miniseries The Great Fire later this year.
Doctor Who has been a BBC staple since its premiere in 1963. The series ran for 26 consecutive seasons, and was revived in 2005. The science fiction drama follows the Doctor, an alien who travels through space and time in the sentient spaceship TARDIS.