Mrs May made the comments ahead of a meeting in Cardiff of the joint ministerial committee (JMC) - the forum for gathering views from around the UK on the process of leaving the European Union.
Nicola Sturgeon has already stressed that she cannot accept a hard Brexit without membership of or full access to the EU’s single market.
However, Mrs May is set to tell her this will not be possible.
“We will not agree on everything, but that doesn’t mean we will shy away from the necessary conversations and I hope we will have further constructive discussions,” Mrs May said in comments released ahead of the meeting.
She added that last week’s supreme court judgment on the need for MPs to vote on triggering article 50 “made clear beyond doubt that relations with the EU are a matter for the UK government and UK parliament”.
The ruling has obliged Mrs May to put the article 50 process, which will trigger departure from the EU, as a bill to parliament.
But the supreme court judges also said the devolved governments could not veto the process.
The subsequent two-clause bill to trigger article 50 is being debated this week and next, and is expected to have been passed before the JMC meets again.
The prime minister said: “The United Kingdom voted to leave the EU, and the UK government has a responsibility to deliver on that mandate and secure the right deal for the whole of the UK.”
The JMC talks will also involve the Brexit secretary, David Davis, and the international trade secretary, Liam Fox, as well as the secretaries of state for Scotland, Wales and Northern Ireland.
After the first JMC Brexit meeting, which was held in October in London, both Ms Sturgeon and Mr Jones said they had been deeply frustrated at the lack of information or apparent plan from the UK government.
Speaking before the Cardiff meeting, Ms Sturgeon said that May appeared set on ignoring Scotland’s desire to remain within the single market.
“It is becoming clearer with every day that passes that the UK government is determined to pursue a hard Brexit and I am determined to do all I can to protect Scotland from the devastating impact that would have,” she said.
“I hope [Monday’s] discussion on this will be meaningful, but the process has been deeply disappointing so far. Time is running out for the prime minister to demonstrate that she is going to uphold the commitment she made to me shortly after taking office that Scotland will be fully involved in discussions to develop an agreed UK approach and listen to alternative proposals for Scotland.”
The new Sinn Féin leader, Michelle O’Neill, is also attending the talks, in the wake of the collapse of Northern Ireland’s devolved administration.
She said May’s government was “seeking to impose Brexit against the will of the people in the north and of the people of Scotland”.
Ms O’Neill said: “The Tory government have effectively set aside the democratic process to pursue their own narrow political agenda. We need all of those opposed to Brexit to stand together.”
Mr Jones - who last week set out a joint white paper for post-Brexit Wales with the Plaid Cymru leader, Leanne Wood, which also calls for continued single market access - said he hoped for “open and frank discussions”.
He said: “I look forward to welcoming government representatives from across the UK to Cardiff. While we know that the UK will leave the EU we don’t yet know how that will happen or what form our relationship with the EU will look like beyond that point.”