Co-pilot Andreas Lubitz, 27, has been blamed for deliberately crashing the flight on March 24 headed from Spain to Germany that killed all 150 people on board.
"We are preparing a lawsuit in the USA and see good chances of finding a judicial venue in the United States," Elmar Giemulla, who represents 39 families of German victims of the crash, told Bild am Sonntag.
The plaintiffs wanted to know "how it was possible that a co-pilot with known mental health problems and a corresponding history was allowed to fly at all," the lawyer was quoted as saying.
The newspaper said compensation in air accident cases in the United States is usually 10 times higher than in Germany.
It was not immediately clear on what legal basis the lawyer wanted the case against the German airline to be heard in the United States.
Giemulla - who told Bild he was in contact with a New York law firm that specialises in aviation claims - could not be immediately reached for comment by AFP.
A Germanwings spokesman said the airline had "no information beyond what is in the press report".
"We won't comment on this press report because we do not believe that the highly individual subject of damages can be discussed in public with the degree of dignity required," he told AFP.
Relatives of many of the 72 Germans among the dead have turned down Lufthansa's compensation offer and accused the airline of ignoring their suffering.
Lufthansa disbursed €50,000 per victim in immediate aid. It has offered €25,000 more to each of the families plus €10,000 to each immediate relative including parents, children and spouses.
The parents of 16 high school student victims in an open letter to Lufthansa CEO Carsten Spohr have charged that to put this value "on the life of each of our children and on our pain" was offensive.
Lufthansa has said its offer had gone "well beyond" what was required by German law.
The airline has said it plans to compensate relatives of non-German victims - among them three US citizens - but that it was too early to quantify the exact amount in all cases because laws differed in their countries of origin.