Kenya currently sit at the bottom of Group F, four points behind the African champions.
"Obviously winning is very important for us at this stage but I don't have to put a lot of pressure on my players. We only need to plan and believe in ourselves that we will succeed," said Amrouche.
But the absence of AC Ajaccio striker Oliech and Origi will be a blow to the side, which remarkably came close to upsetting Nigeria in the reverse fixture in Calabar in March. Amrouche is set to hand the captain's armband to Celtic midfielder Victor Wanyama who has had an impressive season with the Scottish league champions.
Wanyama, who was crowned Scottish Young player of year, is well aware how big the task of leading the team is against the Super Eagles, who have never lost a match to Kenya.
"Nigeria is a strong team. They have gone ten matches unbeaten since the year began but we are confident of giving a good account of ourselves on Wednesday," said Wanyama.
"We are looking forward for the match. It is unfortunate that Oliech and (MacDonald) Mariga will not play. But we fear no one - this is a young team who wants to play and enjoy themselves," he added.