According to the Telegraph, US diplomats have set the deadline of reaching an agreement before the 25th anniversary of the Good Friday Agreement next April.
This would also mean a deal is reached before US President Joe Biden visits next year.
An EU diplomatic source told the paper: “The US is increasing the pressure on the EU now to get the deal done by April. In fact, they are encouraging both the UK and EU.”
The US president, who has spoken of his pride in his Irish roots, is expected to attend an anniversary event of the Good Friday Agreement.
According to the paper, White House officials have privately indicated that he would prefer wrangling over the Protocol to be resolved by then.
Earlier this week, the Government extended a deadline for calling an election in Northern Ireland.
Existing legislation gave parties in Stormont almost six months to form a ministerial executive following the last election in May, which saw Sinn Fein emerge as the largest party for the first time.
The deadline to establish a new executive lapsed on October 28, at which point the Government assumed a legal responsibility to hold a fresh poll within 12 weeks - January 19.
Northern Ireland Secretary Chris Heaton-Harris has extended the deadline for parties to form an executive by six weeks to December 8, with the option of a further six-week extension.
With the Stormont deadlock linked to the dispute over the protocol, the Government move is designed to provide more space for a deal to be struck between Brussels and London.
On Thursday, Prime Minister Rishi Sunak said that he was confident “with goodwill and pragmatism” a deal could be reached on the protocol.
Speaking after he met with Irish Taoiseach, Micheál Martin, Mr Sunak said a “breakthrough” was possible.
Mr Martin also said that UK-Irish government relations had “improved significantly” in recent weeks, and that there was a “window of opportunity” to reach an agreement.