Musa, 25, joined from CSKA Moscow in July 2016 for a then club-record £16.6m but has only made 21 Premier League appearances, scoring two goals.
Sky Sports reports Leicester would want to recoup the majority of that outlay if Musa were to leave this summer.
The Nigeria international spent the second half of last season back on loan at CSKA and his second goal against Iceland has been nominated for goal of the tournament at the FIFA World Cup.
Newspaper reports have also credited Turkish club Galatasaray with an interest in signing the 25-year-old.
Leicester themselves completed the signing of goalkeeper Danny Ward from Liverpool on a four-year deal on Friday.