According to the source, the Foxes are willing to loan Soyuncu provided Fenerbahce agrees to a €20 million fee for Szalai in January.
Soyuncu has only played one Premier League game for Leicester this season and will be a free agent at the conclusion of the season.
If he makes the move, the Turkey international will be expected to play regular first-team football.
Soyuncu looks certain to leave Leicester at the end of the season after failing to get a contract extension and falling out of favor with manager Brendan Rodgers.
Soyuncu, on the other hand, has not indicated a desire to return to Turkey.
If he stays at Leicester during the winter transfer window, the 26-year-old is unlikely to see any playing time.
Szalai joined the Yellow Canaries in 2021 for €2.2 million from Limassol and has gone on to become a big figure, scoring five goals and giving three assists in 90 appearances.
Fenerbahce currently leads the Super Lig with the best defensive record.