However, the Foxes will be hoping they can avoid signing either player by holding onto Maguire, with the Mail on Sunday also reporting that the club are set to offer the defender an improved £75,000-a-week contract as a reward for staying put this summer.
Maguire has attracted the attention of a range of clubs following his commanding displays for England at the World Cup, where he won virtually every aerial duel and scored the opening goal in the Three Lions' quarter final victory over Sweden.
Cahill was also a part of Southgate's 23-man squad for the tournament but hardly featured at all, being kept out of the side by Maguire and Manchester City duo Kyle Walker and John Stones.
It has been suggested recently that Cahill is on the verge of saying goodbye to Chelsea after six years at the club, with the Evening Standard reporting that the Blues set to sell him and replace him with Juventus defender Daniele Rugani.
Cahill is said to be disappointed by the lack of guaranteed playing time under new manager Maurizio Sarri and is prepared to move elsewhere in order to play regularly next season.
Sarri is known to be a big fan of Rugani from his time in Serie A and the club are set to complete a deal for the defender in the coming weeks, having already signed midfielder Jorginho from Napoli.