The delay comes as the United Kingdom grapples with political uncertainty after last week's inconclusive election cast doubt on Prime Minister Theresa May's ability to stay in office or govern effectively.
The formal beginning of the parliamentary session has been delayed due to May's talks with the Democratic Unionists over an informal deal to secure the Conservatives a majority in parliament.
Talks continue with the DUP, a Sky News report said.
It is very unusual for the Queen's Speech to be delayed but in the UK's last government coalition in 2010, the Queen's Speech did not take place until 20 days after the General Election.
"Talks with the DUP have been progressing well and there is broad agreement on the principles of the Queen's Speech", said the source.
It has been pushed back by Downing Street after Mrs May failed to win a majority in the Commons, leaving her frantically attempting to negotiate a deal with the controversial DUP.
The State Opening was initially scheduled for June 19 - the same date when Brexit negotiations were due to begin in Brussels.
On Wednesday, former prime minister Sir John Major, one of the architects of the peace process, said the Government will compromise its impartiality if it enters a confidence and supply deal with the largest Northern Irish party.
"Both parties are committed to strengthening the union, combatting terrorism, delivering Brexit and delivering prosperity across the whole country".
Following her meeting with Mrs May, Alliance Party leader Naomi Long said the PM had "sought to give us her reassurance on neutrality".
At the same time, Michelle O'Neill, the Sinn Fein leader in Stormont, made clear that an agreement on powersharing would require a substantial package of financial support for Northern Ireland from the UK Government.