These reports come as Saints wide man Sadio Mane continually gets linked to a move the other way to Old Trafford despite manager Ronald Koeman refuting claims he and midfielder Victor Wanyama want to move away from St. Mary's.
Januzaj first broke into the Red Devils side in 2013 under former manager David Moyes before falling out of favour under current boss Louis van Gaal. However, the young Belgian has recently featured - and subsequently impressed - upon returning to the United first team.
However, with Manchester United constantly being linked to various forward players, it does appear there could be room for Januzaj to make way on a temporary loan move away from the club.
Southampton's attack has looked toothless so far in their 2015-16 campaign and the addition of new forward-thinking talent will most certainly be welcomed to the South Coast.