Leicester have agreed a club record £10.5million fee for Charles Aranguiz with Internacional - while Gokhan Inler could also arrive.
Aranguiz, 26, played a key role in Chile's recent Copa America triumph and has 40 caps for his country, scoring six goals.
Aranguiz will help strengthen Leicester's midfield following the departure of Esteban Cambiasso.
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The deal will see Aranguiz become the club's record signing, with his transfer exceeding that of Andrej Kramaric, who joined the club in January for in excess of £9m.
Leicester have also moved to further strengthen their midfield by agreeing a fee of £3m for experienced Napoli midfielder Inler.
The 31-year-old has amassed 83 caps for Switzerland and has made 236 Serie A appearances during eight seasons with Udinese and Napoli.
Leicester manager Claudio Ranieri revealed earlier this week he was close to securing a replacement for Cambiasso and now it appears he has found two.
"We are still looking. We are very close with a good player," Ranieri said following his side's 2-1 pre-season victory over Burton on Tuesday.
When asked about the challenge of replacing Cambiasso, Ranieri added: "Yes, of course, because Esteban is a good player, a leader and it is difficult to replace him. But we are looking for him.
"We are very close (with a replacement). But I wait until the end of the window."