Craig Oliver is said to have told The Telegraph that Miller was having meetings about the Leveson report.
[L: David Cameron, R: Maria Miller]
The newspaper had previously claimed that Miller's special adviser Joanna Hindley had tried "to exert improper political influence" on the newspaper over the investigation into the minister's expenses.
"Maria has obviously been having quite a lot of editors' meetings around Leveson at the moment," The Telegraph quotes Hindley as saying.
"So I am just going to kind of flag up that connection for you to think about."
A spokesman for Number 10 said: "My understanding is that she was raising legitimate concerns about the way in which the investigation has been handled, which is perfectly reasonable for her to do that.
"It is reasonable for someone in the Government to raise these kinds of concerns about the way a newspaper is conducting an investigation is a reasonable thing to do."
The newspaper said: "The Telegraph has decided to disclose details of the private conversations amid widespread concern about the potential dangers of politicians being given a role in overseeing the regulation of the press."
Miller wrote to the newspaper to argue that it should not have contacted her parents, adding: "Irrespective of whatever you are investigating, I cannot see a justification for this family intrusion.
"I should be grateful if you could confirm that you now understand the basis of my concern and that on reflection this could have been handled differently."
On Monday, The Telegraph reported that Miller had claimed over £90,000 for a second home used by her parents between 2005 and 2009.