Taoiseach Enda Kenny and Tánaiste Eamon Gilmore both signalled the wish for the British monarch to repeat her landmark trip to the Republic in 2011.
However, it is highly unlikely, the queen would be the royal set to attend the commemoration of the 1916 uprising and war of independence.
The queen spoke fondly of her visit to Ireland when she was seated next to Mr Gilmore at the lavish state banquet thrown in Mr Higgins’ honour at Windsor Castle on Tuesday.
Mr Kenny, visiting London as part of the state visit, said he welcomed the queen’s declaration that her family would “stand alongside” as Ireland commemorated the uprising.
However, he said such decisions would have to be handled with sensitivity. He added that while he would like to see the queen return to Ireland, this was a matter for Buckingham Palace.
The Tánaiste said: “Both the British and the Irish government are very conscious that we should do this together. That we should commemorate the things that we share together, this is a shared history. I think the government will consider issuing an invitation for participation in these events.”
The visit drew controversy in Britain with the attendance at Tuesday’s banquet by the North’s deputy first minister Martin McGuinness.
The queen used her address to pledge that her family and government would “stand alongside” Irish ministers as they marked the anniversaries of the First World War and events leading up to the creation of the Irish Free State in 1922.
The second day of the first state visit to Britain by an Irish president saw Mr Higgins lunch in Downing Street with British prime minister David Cameron.
The president also briefly met London mayor Boris Johnson, as he attended a youth workshop in city hall.
Mr Higgins paid tribute to the many Irish workers in the NHS as he visited staff and patients at University College Hospital, before he gave a speech to the prestigious Royal Society.
On the fringes of the visit, Mr Gilmore met British foreign secretary William Hague, and the Taoiseach attended a business breakfast.
Sabina Higgins had a tour of the Royal Academy of Dramatic Arts which has trained many globally-famous actors. Mrs Higgins also hosted a fashion event intended to showcase the work of Irish designers.
While at Windsor Castle, the president viewed the colours of regiments of the British army disbanded after independence. Duke of York Prince Andrew and the Duke of Edinburgh Prince Philip showed the president the standards of the Connaught Rangers, Royal Munster Fusiliers, Royal Dublin Fusiliers, Prince of Wales’s Leinster Regiment and the Royal Irish Regiment.
Mr Kenny said talks with Mr Cameron had focused on the possibility of a joint trade mission at prime ministerial and taoiseach level in order to boost the economy of both nations.