The Foxes are currently in talks with Porto over a move for Portugal international Pereira, according to the Daily Mail, who will provide strong competition for current right back Danny Simpson.
Pereira has a £33m buy-out clause, but Leicester are aiming to structure the deal differently by offering a lower base fee that will be supplemented with add-on clauses.
The 24-year-old right back is in the Portugal squad for the World Cup this summer and wants to get his future resolved before the start of the tournament. In fact, he hopes to sign for Leicester over the weekend.
Leicester will follow up the signing of Pereira by recruiting Manchester City youngster Patrick Roberts.
The 21-year-old has been on loan at Celtic since 2016 and Leicester are interested in signing the former England Under-21 international as they look to have a busy summer of incomings and outgoings ahead.
Roberts wants to prove himself in the Premier League following his lengthy loan spell at Celtic, and could be part of a deal that sees Riyad Mahrez finally get his big move to Manchester City. A similar deal was discussed between the two clubs on deadline day in January, but talks broke down and nothing materialised.
It resulted in Mahrez going AWOL for several days after reportedly being 'depressed' following his failed move.