Musa has agreed in principle to sign for Fenerbahçe, according to Leceister Mercury.
The Turkish club are said to have started negotiations with Leicester over a potential deal with Musa reported to be happy to leave.
Turkish national newspaper Gunes claim that Musa has been asked if he would be happy to join Fenerbahçe, who finished third in the Super Lig this season, and has said yes.
It would bring to an end an underwhelming season for Musa at Leicester after he struggled to make an impact following a £16 million move from CSKA Moscow last summer.
Despite a stunning brace against Barcelona in pre-season, he managed just four goals in 31 appearances for City, the highlight being a two-goal haul in the FA Cup win against Everton.
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