The Blues boss also says he has a late decision to make on Romelu Lukaku.
New manager Ronald Koeman during the press conference
Defender Williams made the move to Goodison Park last week, but was not deemed ready to take on Tottenham Hotspur after his exertions with Wales at Euro 2016.
Bolasie arrived much sooner after completing his move from Crystal Palace earlier this week.
Swansea's Ashley Williams celebrates scoring their first goal
He featured for the Eagles in their opening game of the season against West Brom so is fit and ready to feature.
And Koeman has confirmed that both could be handed their debuts against West Brom, but he is undecided whether to do so.
"Yannick will be part of the squad. Whether he starts or is on the bench, we will decide,” he told the club’s official website.
“[Ashley] started pre-season later and he has had five days [training at Finch Farm] and is closer to being part of the team. Maybe he will be in the squad.”
Crystal Palace's Yannick Bolasie
The Blues boss has also revealed that it will be a late decision on whether striker Romelu Lukaku features in the game.
The Belgian forward picked up an injury in the Toffees final pre-season game against Espanyol that saw him ruled out of the clash with Spurs.
He was sorely missed as Koeman was forced to name Gerard Deulofeu as his striker for the game and Koeman says it will be a late decision on whether he is ready to start in this game.
“Romelu did his first training session this morning without any problem. I need to make a decision tomorrow if he is part of the squad for Saturday,” he added.
Everton's Romelu Lukaku