According to The National News, QPR had proposed a deal worth more than £6 million (Dh34.8m) to Celtic for the powerfully built central midfielder at the beginning of this week only to be told Wanyama was not for sale.
QPR subsequently readjusted their targets and are working on a deal for the Cameroon international Stephane M'Bia.
Wanyama was told of Celtic's decision ahead of a crucial Champions League qualifying tie with Helsingborgs on Wednesday.
Although upset at being denied the opportunity to fulfill his ambition to become the first Kenyan to play in the Premier League, the 21 year old resolved to focus on the European tie, and scored in a 2-0 victory.
Extensively scouted by Arsenal, Manchester City and Manchester United among other major Champions League sides, Wanyama is expected to be the subject of further offers in the January window.
The quality of his play both in his preferred position as a holding midfielder and in the centre of defence coupled with a relatively low wage influenced Celtic's decision not to sell.
Though five years older than Wanyama, M'Bia shares several characteristics with his fellow African, and is also capable of playing in front of the defence or operating in the heart of it.