The Nigeria international has dropped down the pecking order at Leicester after this season's management upheaval.
Slutsky remains keen on Musa, admitting earlier this season a deadline day deal fell through.
"We came very close to Musa," Slutsky told the Hull Daily Mail. “But not each decision depends on me or the club.
“I think maybe he wants to prove himself at Leicester and he needs one more attempt. He thought a lot and finally his decision was to stay at Leicester.
“The final decision was at midday on deadline day and we didn't have a chance to change Musa for another option."