Carvalho, 28, was reported to be in advanced talks with the Foxes back in June.
Despite the silence since then, the deal is still on course with Leicester ready to pay around €25m for William.
His former club Sporting CP will receive 25 per cent of the fee as part of the settlement they negotiated two years ago.
William is a fan favourite at Betis and will finish the season in Andalusia before speeding up his Premier League move.
The combative midfielder quit Sporting for Betis in 2018 and has made 52 appearances in all competitions.
Injuries have limited him to 13 La Liga appearances this term, but he impressed against Atletico Madrid on Saturday.
Carvalho has been capped 59 times by Portugal and was part of the side that won Euro 2016.