Max Goeldi, a Swiss national who sought refuge at his country's embassy in Tripoli, has offered to turn himself in to Libyan authorities, his lawyer says.
Earlier sources told Al Jazeera that Libya had given the Swiss embassy in Tripoli until 12 noon on Monday to hand over Goeldi.
Mousa Koussa, the Libyan foreign minister, reportedly issued the ultimatum to European diplomats on Sunday.
Goeldi was sentenced to four months in jail by a Libyan court for having allegedly overstayed his visa and conducting illegal business activity.
Following the Libyan government's ultimatum, Salah Zahaf, Goeldi's lawyer, told the AFP news agency: "He will leave the embassy and turn himself in voluntarily," .
Zahaf said he expected Goeldi to be taken to Ain Zara prison near Tripoli.
He also said the defence plans to ask the court for an amnesty.
Relations between Libya and Switzerland have been strained since July 2008, when Hannibal - a son of Muammar Gaddafi, the Libyan leader - was arrested in the Swiss city of Geneva after two workers complained he had mistreated them.
The row escalated when Libya swiftly detained Hamdani and Goeldi and confiscated their passports.
It deteriorated further last year when a tentative political deal between Swiss and Libyan ministers fell through.