The 25 year old spent most of the 2017-2018 season on loan to CSKA Moscow. Musa made 10 appearances with the Russian side and scored six goals.
The Nigerian international has made eight appearances this year and scored two goals.
Musa has two years left on his contract with Leicester City, however Claude Puel has deemed the forward surplus to requirements and this will be the perfect time for the club to sell him.
Having attracted interest from many after his performances with Nigeria in the World Cup. There is also interest from newly promoted Fulham and also from Turkish side Galatasary.
The Turkish side are looking to sign Musa on loan for a season, with the option to sign permanently next summer.
Signing Musa would be a great addition to the Terriers and David Wagner will be hoping to be able to avoid relegation from the top flight for a second season.
Once again Huddersfield are already one of the favourites for the drop with the bookies, in what is generally know as "second season bounce".
Having made a few signings over the summer so far, with the biggest spend being on Terence Kongolo from AS Monaco, the Terriers are still in search of players to strengthen the squad.
During the world cup campaign Musa showed sublime skill, his first touch for the goal brought down a cross and fired it home, the second goal showed composure.
The skill of the Nigerian would certainly help the Terriers in the goal area, one of the areas Huddersfield Town struggled with last season.
Lack of goal scoring saw the Terriers only avoid relegation by four points. The Yorkshire club will be looking to improve on last season, and hope to finish higher with more goals scored than last season.
The Nigerian also possesses pace in abundance, and his willingness to make direct runs in behind the opposition's defence is an attribute that many clubs will find appealing.
The assest to any club that signs Musa can only be good. Musa could be close to signing for the Terriers now that the Nigerian side were knocked out of the World Cup in Russia