Kemi Badenoch will have to rebuild the Tory party if she becomes leader and will need to “pivot” by talking to those who are not “diehard Tories”, Conservative peer Ruth Davidson has said.

Baroness Davidson told Beth Rigby on the Electoral Dysfunction podcast Ms Badenoch, who is in the final two of the Conservative leadership contest, will have to look outside core Tory voters to rebuild the party.

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She said the fact that Ms Badenoch chooses to appear in media “that is very much considered to have a high proportion of people that are already Conservative members and voters” – such as The Telegraph, the Daily Mail, the Daily Express and GB News – betrays “certainly a lack of confidence”.

“This is somebody that is going to have to rebuild the Tory party and they’re going to have to do it by talking beyond people that are already diehard Tories,” Baroness Davidson said.

“If she wins, she needs to pivot. She needs to pivot fast.”

The Conservative peer and former leader of the Scottish Tories said Ms Badenoch, the former business secretary, “clearly thinks she is winning and she doesn’t have to chase it”.

Ms Badenoch has made few appearances during the campaign compared with her competition, Robert Jenrick, who has been holding rallies, doing TV and newspaper interviews and has made sure he is highly visible on social media.

“Robert Jenrick clearly thinks that he’s got work to do, and that the more people see of him, the more they will like him,” Baroness Davidson said.

“I think the assessment that’s been made by Kemi’s camp is that there is merit, and there’s often merit in being slightly blank, a slightly blanker page that people can project what they want onto – so that people think that she is their type of Tory and one that they would be comfortable voting for.”

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The Tory peer added “it’s a sign of both confidence and not confidence” she is not doing much media.

“Confidence that she’s already in the lead, not confidence, and she thinks that if people see more of her, she might lose that lead,” she said.

Baroness Davidson previously revealed she voted for James Cleverly, the former home secretary and foreign secretary who was knocked out of the race last week amid accusations of vote lending.

Baroness Davidson said she thought it was likely that Mr Cleverly would receive a job in the shadow cabinet.