The new airline would, according to Bild daily newspaper, be up and running by the beginning of 2013. Its current sister airline – Germanwings – would be scrapped and some of the planes rebranded Direct 4 You. Staff would be given the option to move to the new company.
By 2015, another of Lufthansa's subsidiaries, Eurowings, could be merged into the new fleet, the paper said.
Many intra-European flights that Lufthansa currently operates could be adopted by Direct 4 You, which, according to Bild, should be offering flights from €49 on its fleet of 90 airbuses.
Lufthansa denied the report on Friday, saying the Direct 4 You concept was not planned to be a new budget airline.
The company was planning to merge Germanwings with its decentralised European services which do not fly from Munich or Frankfurt, some of which are served by Eurowings. It could well be that Eurowings and Germanwings will not in the future provide flights on the same routes, a spokesman said.
Lufthansa's financial woes have been in the media recently, with reports suggesting that it plans on making cuts of up to €1.5 billion as it faces increasing competition.
As a result of the cuts, its fleet of planes would, according to Die Welt daily, mostly fly out of Frankfurt and Munich, two of Germany's biggest airports.
The new company has not been given the final go-ahead from the Lufthansa board, and the airline is yet to release any official information about the venture.