The Porto defender is reportedly keen to secure his future ahead of the weekend, as he is set to join up with the Portugal squad for World Cup training next week.
According to 'Sportsmail', negotiations have been ongoing with the Portuguese club to settle on a lower fee than his buy-out clause of £33million, plus add-ons.
Pereira has caught the attention of several Premier League outfits including Manchester United and Spurs, but it is Leicester who have been most persistent in their attempt to sign him.
Leicester are also aiming to gain Manchester City winger Patrick Roberts in a move that would see Riyad Mahrez depart to the Premier League champions.
Mahrez was initially tipped to join Guardiola's side in January, but negotiations fell through after the clubs struggled to agree on a price, leaving the midfielder disappointed.