The Luton-based airline is working on a series of options for the business, according to Sky News, including a sale or restructure of its short-haul business through a joint venture or feeder deal with another airline.
Sky News suggested that Jet2.com or easyJet could be interested in such arrangements, but both airlines said they could not comment.
Monarch, which is due to renew Atol for its package holidays at the end of this month, could change its strategy to concentrate on long-haul flights.
The airline, which is owned by Greybull Capital, has been affected by a price war in the short-haul market this year as major competitors such as Ryanair have slashed their fares to fill their seats.
“In recent months we have undertaken, and continue to undertake, a comprehensive review of Monarch designed to determine its optimal future shape, size and strategy,” said Monarch in a statement.
“We are having regular discussions on a number of options with potential strategic partners and we will announce any material developments, if and when they happen.”