The Nigerian struggled to establish himself at the King Power Stadium and was shipped out on loan to CSKA Moscow during the January window.
However, Musa has impressed during the World Cup finals, scoring twice during his team's 2-0 win over Iceland in the group phase.
Several clubs, including Wolverhampton Wanderers, have since been linked with the winger, while CSKA have revealed that they are keen to secure his services on a permanent basis.
According to 90min, Fulham and Huddersfield are readying counter-offers.
The Nigerian international scored seven goals in 16 appearances for the Russian outfit.