The Baggies are in talks with the Brazilian forward over a fresh contract on significantly improved terms, aimed at rewarding his efforts since first arriving at the club on loan last year.
Pereira scored eight goals and provided 16 assists last season to help Albion win promotion back to the Premier League.
The 24-year-old initially joined the Baggies from Sporting Lisbon on a loan deal with an obligation to buy, which also included the terms of his current contract, thought to be worth around £30,000-a-week.
But Albion are now willing to offer terms which more accurately reflect Pereira’s importance to Slaven Bilic’s team, with a £45,000-a-week offer putting him closer to the club’s existing top earners.
The new agreement will also see an extra year added to his four-year contract, with negotiations having taken place outside the transfer window.