Inter Miami are searching for a new goalkeeper ahead of the 2021 MLS season, which looks set to start in March.
They decided against extending the contract of veteran Luis Robles and the 36-year-old subsequently announced his retirement.
The Miami Herald claim the club have opened talks with Everton over a deal to sign Denmark international Lossl.
He is said to be keen to quit Goodison Park after falling down the pecking order to third choice following Robin Olsen's arrival last summer.
The report also states that Lossl is keen to book his place in the Denmark squad for the European Championships and would like regular football to achieve this.
Lossl joined Everton on a free transfer in July 2019 but is yet to make a first team appearance for the club.
He started his career at FC Midtjylland before moving to Guingamp, Mainz and then Huddersfield.
The 31-year-old may not be the only person with an Everton connection at Inter Miami in the near future.
Beckham has reportedly held talks with former Man United and Toffees player Phil Neville over becoming the club's next manager.
David Beckham's MLS franchise Inter Miami are reportedly in talks with Everton to sign goalkeeper Jonas Lossl.
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