Hull have held talks with Leicester City this week and are confident of finalising a move before the deadline on Thursday.
This would see Musa reunite with Tigers boss Leonid Slutsky, who the City forward played under for four years at CSKA Moscow.
The 24-year-old has struggled to impress since his £16million move to Leicester last summer and has scored just five goals in 33 appearances.
Musa did find the net in the Carabao Cup victory at Sheffield United but had endured a torrid first-half performance at Bramall Lane.
“He is not our player but, of course, every coach is better working with players he knows and I worked with Musa for four years,” said Slutsky. “I know him and he knows me.”
Musa’s finest performance for Leicester still remains the International Champions Cup game against Barcelona, where he scored twice.
Musa also scored twice in the FA Cup victory over Everton last season.