The project, which will pipe 16 billion cubic metres (bcm) of gas from Azerbaijan's Şahdeniz II field, is seen costing between $5 billion and $7 billion and construction is expected to start at the end of 2013 or in early 2014.
"The work has entered its final stage. The inter-governmental agreement is expected to be signed in İstanbul next week," a senior Turkish official told Reuters.
Another official said the signing ceremony could be held on June 26 with the attendance of Prime Minister Recep Tayyip Erdoğan and Azeri President Ilham Aliyev, but may be delayed by a few days.
Turkey has a 20 percent stake in TANAP, while Azerbaijan's state oil company SOCAR holds 80 percent. In March, a Turkish Energy Ministry official said Turkey may raise its 20 percent stake in the project.
Under the project, some 10 bcm of gas is planned to be shipped to Europe, while Turkey will get the remaining 6 bcm.
Analysts have said TANAP could undermine efforts to bring online the 7.9 billion euro Nabucco pipeline project, which aims to ship 31 bcm of Caspian and Middle Eastern gas to Europe.
Turkish officials have said Turkey will continue to be a part of Nabucco.
Austrian energy group OMV is counting on a shorter version of the Nabucco pipeline to win the business of carrying gas to Europe from Azerbaijan, Chief Executive Gerhard Roiss told Reuters last week.