Southampton were reportedly rivalling Leicester City and Manchester United for the CSKA Moscow striker.
The striker has been linked with several clubs in in the January transfer window, with Leicester City currently those pushing hardest for his signature.
Southampton were also said to be interested, with the Mirror reporting that they had an enquiry for the player rebuffed over the weekend.
However, it seems that a move is not on the cards, with manager Ronald Koeman saying he has completed his business and Musa is not on their radar.
"We did our job with Charlie Austin,” he told BBC Sport.
“I think if you have to do your business today then you are nervous or you don't know what you have to do.”
"I know the player [Musa] but he was and is not on our list."
While a move at the end of the January transfer window is now off the cards, there is every chance the Saints could return in the summer.
Graziano Pelle looks destined to leave the club at some point, with a return to Italy having been mooted and the arrival of Charlie Austin making it all the more likely.
His exit would leave Koeman short up front though, and perhaps he could revive interest in Musa as a replacement, should he not head elsewhere before then.