The actress has been prevented from signing up for the drama because BBC One controller Danny Cohen wants her to focus on her sitcom Miranda, The Sun claims.
Doctor Who creator Steven Moffat allegedly offered Hart a "significant role" that she was hoping to accept.
"Miranda was thrilled to be asked to be on Doctor Who," a source claimed. "Steven offered her a decent role and she felt, as it was on the BBC, there would be no problem.
"But the BBC One controller let it be known that he wants her focused on her show, which he has nabbed from BBC Two. Miranda's gutted as she feels she could do both."
Miranda was promoted from BBC Two to BBC One earlier this year but the third series will not be broadcast until 2012.
Hart recently signed up to star alongside Jenny Agutter in the new BBC One drama Call The Midwife, which will also air next year.
Watch a teaser trailer for the return of Doctor Who below: