The Daily Mail claim that Foxes manager Claude Puel is still looking to bolster his squad with just seven days of the transfer window remaining, and seems to have turned his attention to the Belgian international.
While Jose Mourinho's side are understood to have a buy-back clause for the 23-year-old, they appear unmoved in wanting the bring the winger back to Old Trafford, leaving the door open for Leicester to make their move ahead of their Premier League opener, ironically against United.
Despite bursting onto the scene for the Red Devils in the 2013/14 season, Januzaj never consistently showed the level of talent people expected of him, with loan moves to Borussia Dortmund and Sunderland failing to bring out the best in him.
He currently plies his trade in La Liga for Real Sociedad after being sold by Manchester United in the summer of 2017 for an estimated £9.8m, scoring four goals and providing six assists in all competitions last season.
His form earned him a place in Roberto Martinez's Belgium squad for the recent World Cup, even managing to score the winner in their final group game against England in what was his only appearance at the tournament.
Leicester have been busy already this summer, bringing in James Maddison, Jonny Evans, Ricardo Pereira and Danny Ward in this window, with the moves somewhat financed by the £60m sale of talisman Riyad Mahrez to Manchester City.