The deal could be worth more than $10 billion for the two aircraft makers, the paper said.
United sent a formal request to Boeing and Airbus on Tuesday, the paper said, citing people familiar with the matter.
The request focuses on replacing many of the 111 aircraft in United's wide-body fleet, as well as some of its 97 aging Boeing 757 narrow-body planes, the sources told the paper.
United could sign a major order as early as the fall if Boeing or Airbus agree to certain conditions, the paper said.
However, the financing arranged by the manufacturer that doesn't eat into United's cash would be the most crucial, the paper said, citing people familiar with the matter.
United has hired aviation consulting firm Seabury Group LLC to help it negotiate with the plane makers, the paper said.
A spokesman at Airbus said he was not aware of this particular deal but added the firm was talking to its customers all the time.
Reuters could not immediately reach United or Boeing for comments outside regular hours.
(Reporting by Ajay Kamalakaran and Esha Dey in Bangalore; Editing by Greg Mahlich)