Devolution would not work without the inclusion of the party, he said, which represents the majority of republicans in Northern Ireland.
Ian Paisley's Democratic Unionist Party says the British and Irish governments are too soft on Sinn Fein. It has demanded the peace process move on without the party, with which it insists it will not share power until its paramilitary wing, the IRA, renounces all violence and criminality; something the DUP says will never happen.
But the Northern Ireland Office official, who requested anonymity, told press in London that "the door will always be open" to Sinn Fein and there was no time limit for their inclusion.
It was now up to the IRA to respond to Sinn Fein Leader Gerry Adams' call for them to lay down their weapons, he said.
The British government was hopeful the IRA would agree to do so and that power-sharing negotiations could then resume in the summer, he concluded.