Murdo Fraser, the party's finance spokesman in Holyrood, claimed there was “no support” for the SNP’s manifesto pledge to break up the United Kingdom.
The Prime Minister will make it clear that the union is an “unstoppable force” whose strength will be needed during the talks.
Ms Sturgeon, the Scottish First Minister, has constantly called for a second independence referendum ever since Mrs May announced her intention to leave the European single market – something the SNP believe is crucial to the Scottish economy.
Murdo Fraser told Nicola Sturgeon to forget her dreams of Scottish independence
There is absolutely no evidence the Scottish people want a re-run of the independence referendum
Speaking on BBC Radio 4’s Today programme, Mr Fraser slated the Scottish leader, insisting she will not be able to fulfil her party’s manifesto promise.
“Theresa May is not saying there should never be another referendum,” he said. “What she is saying is now is not the time, we’re engaged in the Brexit process.
“Let me make this important point, in saying that she is entirely in tune with Scottish public opinion because there is absolutely no evidence the Scottish people – who have been consistently asked this question in opinion polls – want a re-run of the independence referendum, which was held less than three years ago.”
The programme’s host Nick Robinson argued the SNP had been voted in based on their support for Scottish independence and will have to continue to their pursuit.
Mr Fraser added: “They went into that election with an overall majority in the Scottish Parliament, and came out of the elections having lost their overall majority.
“They don’t have a majority within the Scottish Parliament based upon that manifesto – there is not public support for another independence referendum, at this time.
“We were told back in 2014, when we had the vote, that it would be a once in a generation vote. Nicola Sturgeon even said it would be a once in a lifetime vote – I don’t know how long a generation these days, but two and a half year seems an awfully short time.”
The Prime Minister, prior to her Monday meeting with Ms Sturgeon, told the Scottish First Minister she would not sanction a second vote until Brexit is complete.
Nicola Sturgeon's most outrageous quotes Mon, March 13, 2017
The nationalist chief always has plenty to say
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'Men – the colour of their tie is the most difficult decision they have to make every day'
Mrs May infuriated the Scottish lead, by rejecting her demand for a referendum between autumn 2018 and spring 2019, insisting “now is not the time’ for the vote.
On the final leg of her UK tour, Mrs May will appeal to the union's shared values and sense of history to confront the demands for independence, saying Britain has a “proud shared heritage”.
She will say: “And on that foundation, we have built a country where we share the challenges that we face, and bring all the expertise, ingenuity and goodwill we share across this anon to bear to tackle them.
“So as Britain leaves the European Union, and we force anew role for ourselves in the world, the strength and stability of our union will become even more important.”