Ruth Davidson has refused to rule out becoming an MP or even the Conservative party's UK leader.
But she said that the new powers being devolved to Holyrood meant MSPs currently had "a lot more to do" than backbench Scottish MPs.
The Tories currently have no backbench MPs from Scotland - the party's sole MP north of the Border is the Scottish Secretary David Mundell.
Ms Davidson, 37, became engaged to her long-term partner Jen Wilson, 34, during a trip to Paris at the weekend, and later described herself as “very happy”.
READ MORE: Scottish Conservative leader Ruth Davidson gets engaged to long-term partner
David Cameron congratulated the couple, saying that he was “delighted for them".
Earlier this month Ms Davidson led her party to a stunning result in the Holyrood elections, more than doubling the number of Tory MSPs from 15 to 31.
The party also beat Labour into a humiliating third place.
But in an interview with The House magazine she struck a cautious note, saying: “I think the tales of our demise were overspun, but then so are tales of our renaissance.”
Many of the party's voters this time around had not guaranteed to back them at future elections, she said.
She did not rule out becoming an MP one day.
READ MORE: Scottish Conservative leader Ruth Davidson gets engaged to long-term partner
She said: “I’m certainly ruling it out for now because I’ve got a pretty bloody big job.
"There is also the question, with all the new powers coming to the Scottish Parliament, MSPs have a lot more to do than backbench MPs from Scotland do now.
"In terms of wholly devolved health, wholly devolved justice, wholly devolved education, mostly devolved transport, large parts devolved welfare, large parts devolved taxation.
“It’s now because a bigger and much more interesting job to be an MSP than it is to be an MP from Scotland sitting on the backbenches.”
Asked if being Prime Minister some day appealed, she said: “I’m in a hugely privileged position in that I get to regularly see behind the door at Number 10, and it looks like the loneliest job in the world and I do not seek it.”
She also described the EU referendum as a “cost/benefit analysis”.
And she also suggested that Justice Secretary Michael Gove would play a crucial role in healing the Tory party after the European Union referendum.
“I think somebody like a Michael Gove figure is very important in bringing the party back together, in terms of the Cabinet coming back together,” she said.
“We shouldn’t also forget the belief in duty and service that people in the Conservative Party have, and that includes our activist base and ordinary members.
READ MORE: Scottish Conservative leader Ruth Davidson gets engaged to long-term partner
“Don’t underestimate the sense of duty that Conservatives have to make sure we continue as a government. Because if not us, my God it can’t be the other lot given the state they’re in.”
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