Martin McGuinness has said that he would be open to meeting the Queen, adding that the Queen's visit to the Irish Republic last May made an impression on him.
If the meeting happens it will mark the first time since the Sinn Fein party was created in 1905 that the leadership has agreed to met with a British monarch.
The Sinn Fein Deputy First Minister attended an event to promote Northern Ireland at St James' Palace in London during the week.
"I've made it clear that the visit of Queen Elizabeth of Britain to the South was something that we looked at with considerable interest," he said, according to the Irish Independent.
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"And I think the fact that she was prepared to recognise the importance of the Irish language; that she was prepared to stand in a very dignified way to honour those patriots who struggled in 1916 to bring about a free and independent 32-county Irish Republic, that made an impact upon me.
"So that's an issue that I will ponder and I wouldn't rule anything out."
Sinn Fein did not take part in any of the main ceremonies when the Queen made her first visit to the Republic last spring.
However, last September, during the Irish presidential election, McGuinness said, that if he were elected president, he would meet all heads of state "without exception."
McGuinness was interviewed for the BBC's Inside Politics programme on Sunday.