ANSA news agency reported citing informed sources that the Italian warship was now on course to intercept the vessel early on Saturday.
The report did not explain exactly how the vessel was able to escape.
The ship, the Asso 22, had 11 crew members including eight Italian nationals on board when it was seized in Tripoli last month on the same day that air strikes by an international coalition including Italy began.
The other crew members at the time were two Indians and one Ukrainian.
The 75-metre (246-foot) long anchor handling tug vessel belongs to the Naples-based oil industry shipping business Augusta Offshore.
There have been intensive diplomatic efforts to get the ship released, with Italy earlier saying the crew were being held as "hostages".
The ship had arrived in the port of Tripoli to ferry workers from the Libyan state oil company NOC when armed men climbed on board.