Carole Ghosn was banned from meeting her husband after his release on bail because of fears she might help tamper with evidence.
Lebanon and Japan do not have an extradition treaty and Japanese justice officials acknowledge it is unclear whether the two can be brought back to Japan to face any charges.
Prosecutors have said they did not want Ghosn to be granted bail because they saw him as a flight risk.
In Beirut, the justice minister confirmed that prosecutors had received a “red notice” arrest warrant from Interpol in respect of Ghosn and would take the necessary action.
But the ministry said nothing had been received from Japanese prosecutors relating to an arrest warrant for his wife, Carole, who is in the Lebanese capital.
Earlier on Tuesday, Ghosn’s former employer, Nissan, said it was still pursuing legal action against him despite his escape.
The Japanese car maker said in a statement that he engaged in serious misconduct while leading the Nissan-Renault-Mitsubishi alliance.
“The company will continue to take appropriate legal action to hold Ghosn accountable for the harm that his misconduct has caused to Nissan,” it said.
Ghosn managed to skip bail and leave the country despite surveillance while he was staying at a home in Tokyo.
He is scheduled to hold a news conference on Wednesday, his first such appearance since his arrest in November 2018 and his dramatic flight to Lebanon, his childhood home.
He is expected to detail some of the claims he has made against Nissan since his arrest.