It was reported at the start of August that the Foxes had agreed a £3million deal with Napoli for the Switzerland international and were closing in on his signature.
However, Sky Sports claim there are other clubs interested in the 31-year-old, leading to a delay in him deciding whether to join Claudio Ranieri’s side, who have won both of their opening Premier League games.
Inler joined Napoli from Udinese in July 2011 and has been capped 83 times by Switzerland.
Foxes coach Kevin Phillips told talkSPORT regarding Inler earlier this week: “I believe there may be something happening this week but that department isn’t really down to me.
“We have bought the boy N’Golo Kante in. He came on the other week and did very well, but that is an area we are looking to add maybe one or two more players before the window shuts.”