The former Work and Income NZ boss, who is the party's chief executive, announced yesterday that she would stand for the Conservatives in the electorate.
But Mr Key has already signalled that National voters in Epsom should give their electorate vote to Act Party candidate David Seymour.
On TVNZ's Breakfast show this morning, Mr Key said he was not concerned the Conservatives might take away some voters.
"No. Look, I like Christine -- she's a really good lady, I've known her over the years and she's a sensible person. But in the end, she doesn't have a dog show at Epsom," he told Breakfast.
"We poll there. What I can tell you is our polling shows about 70 per cent of Epsom voters are going to give their party vote to National.
"A fair few of them I suspect will give their electorate vote to David Seymour and Act, because they want to vote tactically and see the return of a National-led Government.
"Of course small parties are going to do things like this because it means you and I are talking about it this morning, and that's always good for a small party. But she's got no chance of winning Epsom."
Ms Rankin, however, is confident she will win, and has no concerns over splitting the right vote.
In announcing her candidacy yesterday, she took a swipe at the National-Act deal, saying that Epsom voters have "integrity".
"They don't have to be told what to do. They're not dummies."
Mr Key has ruled out a deal with the Conservatives, meaning it would have to gain at least 5 per cent of the party vote to enter Parliament -- a feat that Act does not have to achieve.
Mrs Rankin came out swinging for a National-led Government, which could be seen as a pitch to David Seymour voters.
"National needs the Conservatives to give them a backbone, and keep them on a short leash," she said.
She denied she was trying to win votes off Mr Seymour, saying she was "not interested in Act".
Mrs Rankin said internal polling showed the electorate was socially conservative, with drug and alcohol policy being the biggest concern. She wanted the drinking age returned to 20, and a total ban on so-called legal highs.
- Derek Cheng of the NZ Herald and APNZ
