The report states the Foxes have stepped in with an offer for the 26-year-old, despite interest from larger European clubs, as Claudio Ranieri sees him as the ideal replacement for the influential Esteban Cambiasso.
Aranguiz is currently contracted to Internacional and has been ever-present for the Brazilian side since his move from Universidad de Chile in 2014.
How likely is this potential transfer deal?
According to Sports Bild, Bayern Leverkusen are closing in on a deal for the diminutive midfielder and look to be at the front of the queue for his signature.
The Bundesliga side are among the biggest clubs in Germany and it would be seen as a good move for the Chilean should he sign for them before the transfer window closes.
Leicester could find it hard to convince the player that his future lies in the East Midlands rather than Germany, should they get a chance to talk to him before he commits to a move.
The Foxes will be looking to bring in good players this summer, helped by the pull of the high-profile Ranieri, but this potential deal looks highly unlikely.