Sueddeutsche Zeitung, citing unidentified corporate sources, said talks were not close to a conclusion and the process could take some time.
The three airlines, all members of the Star Alliance, declined to comment.
TAP, which was partly privatized in 2015, is 50%-owned by the Portuguese state. Private consortium Atlantic Gateway, led by Brazilian-U.S. airline mogul David Neeleman, has a 45% stake. TAP employees hold the remaining 5%.
Lufthansa earlier on Wednesday announced a cost savings programme, including a suspension of new recruitment, to counter the business impact of the coronavirus outbreak.
Reporting by Ilona Wissenbach in Frankfurt, Andrei Khalip in Lisbon, and Tracy Rucinski in Chicago; Writing by Tom Sims; Editing by Mark Potter