The two shows have been preliminarily placed on BBC One and ITV1's Christmas Day lineups and are expected to overlap slightly in the evening.
Speaking after a screening of the Call the Midwife special yesterday, show stars Raine and Helen George dismissed talk of a rivalry between the two ratings hits and claimed that they would prefer if the two programmes didn't force viewers to pick between them.
"I think it's wonderful now with Sky+ that viewers can watch everything," said George. "Doctor Who, Downton and Call the Midwife, everything."
Raine said: "I don't think they'll ever put us head-to-head, I think that would be so stupid.
"I love Downton and I don't see it as a competition."
She also revealed that the show's casts had bonded on a joint trip to the US for press junkets.
"We were on the same plane to a PBS convention for the new TV season. We were on the plane with Jo Froggatt and Brendan Coyle and I was bounding up to them asking, 'Hi, are you guys here for the PBS thing?'
"They are really lovely and really nice. And apparently they like our show as well. So it's a mutual love."
Call the Midwife is the BBC's biggest drama hit of 2012, scoring record ratings in January.
Based on the memoirs of Jennifer Worth, the 1950s East End drama stars Miranda Hart, Pam Ferris and Jenny Agutter.