The 19-year-old made his debut for the Hammers during a Europa League game at the start of this campaign.
The defender - who primarily plays as a right-back but can also feature in a more central role - made his debut for the Hammers when he started their Europa League clash with Astra Giurgiu in August, but he has not featured for the club since the defeat in Romania.
And with Sam Byram arriving at the Boleyn Ground from Leeds in the last few days, it appears that Bilic is confident that he has more than enough depth in his squad to allow the 19-year-old to join Mixu Paatelainen's side for the rest of this campaign.
The Scottish Sun reports that Knoyle is set to replace Ryan McGowan, who has agreed a deal to join Chinese side Henan Jianye.
Knoyle will be hoping that his arrival lifts the club, given their desperate situation in the league. They currently sit bottom of the table, 13 points adrift of safety, so need Knoyle to have an immediate impact.