Irish President Mary McAleese has said a royal visit to the Republic of Ireland will only happen once policing and justice powers are devolved.
The Queen met the Irish president at Queen's University
Mrs McAleese was speaking after meeting the Queen at Queen's University in Belfast on Wednesday.
"I think the day is significantly closer. We know it is dependent on the completion of devolution," she said.
The visit would be the first by a British monarch since the island of Ireland was partitioned in 1921.
Mrs McAleese said: "We are not entirely sure what the timescale is. We hope it will keep closely to the timetable.
"When that is done, when devolution is completed, I think then anything is possible."
Mrs McAleese's comments have been criticised by the DUP, which accused her of "using the visit to make a political statement".
"It seems that almost every time she makes a comment about Northern Ireland she actively seeks to antagonise the unionist population," the party's Upper Bann assembly member Stephen Moutray said.
"The DUP is under no obligation to agree to the devolution of policing and justice powers to Stormont."
However, Deputy First Minister Martin McGuinness said difficulties around the devolution of these powers could be overcome.
"The (new DUP) leader, alongside myself and Gerry Adams will have to deal with these potentially difficult situations," the Sinn Féin MP said.
"We all know that we are in a process that, if we can¿t reach agreement, we are going to be in big trouble."
The Queen had a private meeting with Mrs McAleese at the elder of Northern Ireland's two universities. She also talked with Nobel Laureate poet Seamus Heaney.
The meeting took place on the second day of a three-day visit by the Queen to Northern Ireland.
Earlier on Wednesday, the Queen accompanied by the Duke of Edinburgh visited the East Belfast Mission on the Newtownards Road.
On the street outside, hundreds of people, many waving union flags, cheered on the visitors.
It is the 20th time the Queen has been in Northern Ireland
On the way into the mission the royal visitors were greeted by Lady Carswell, the Lord Lieutenant of the County Borough of Belfast, before meeting First Minister Ian Paisley and Rev Garry Mason.
Inside, the Queen met mothers and children from the mission's parent and toddlers group and heard about plans for a £20m regeneration programme for the mission.
The Queen met Ian Paisley in east Belfast
She unveiled a plaque to commemorate her visit before accepting a posie of flowers from six-year-old Erin Dawson.
At Queen's university, the Queen heard a poem written by Mr Heaney commemorating the 100th anniversary of learning at the institution.
She was also shown exhibitions about the university's achievements.
QUB Vice-Chancellor Professor Peter Gregson described the university as "one of the best in the UK for knowledge transfer".
"I have no doubt that the coming years will see a growth in the number of spin-out companies and high-quality jobs associated with them," he said.
On Thursday, the Queen will attend the Maundy Service in Armagh Cathedral.
She attended a reception at Hillsborough Castle on the first day of her visit.
In her first engagement at Hillsborough Castle, the Queen met more than 300 members and workers from the Territorial Army.
The event was to mark the organisation's centenary.