But the new Prime Minister insisted Scots had “had their vote” on independence and the issue should not be on the table.
Mrs May met First Minister Nicola Sturgeon at Bute House yesterday on one of her first engagements since taking over as premier on Wednesday.
Afterwards she said it had been “an excellent meeting” and she looked forward to future “constructive and positive discussions”.
The referendum vote in favour of the UK leaving the European Union was inevitably the key topic for the two leaders.
Ms Sturgeon has warned that a second independence referendum is “highly likely” if no way can be found to preserve Scotland’s relationship with the EU.
Mrs May said: “I’m willing to listen to options and I’ve been very clear with the First Minister today that I want the Scottish Government to be fully engaged in our discussion.
“I have already said that I won’t be triggering Article 50 until I think that we have a UK approach and objectives for negotiations – I think it is important that we establish that before we trigger Article 50.”
Asked about the possibility of a second independence referendum, she said: “As far as I’m concerned, the Scottish people had their vote – they voted in 2014 – and a very clear message came through. Both the United Kingdom and the Scottish governments said they would abide by that.”
Mrs May said she wanted to ensure her first visit as Prime Minister was to Scotland because “Scotland is important to me”.
Ms Sturgeon said: “I was very pleased Theresa May said she was absolutely willing to consider any options the Scottish Government now bring forward to secure Scotland’s relationship with the European Union, that the process that now takes shape by the UK government will be open and flexible, and that the Scottish Government will be fully involved in that.
“I have been very clear that we have to make sure that Scotland’s interests are protected and I want to examine every option of doing that.”
But she added: “It would be inconceivable for any prime minister to seek to stand in the way of a referendum if that is what the Scottish Parliament voted for, and we have heard from other Conservative politicians in the past few weeks that that would be the wrong thing to do as well.
“So I work on the basis that trying to block a referendum, if there’s a clear sense that that’s what people in Scotland want, would be completely the wrong thing to do.”