The Scottish Daily Record reported the trio value the 20-year-old at 8 million pounds (Sh1.056b) well short of the 14 million (Sh1.84b) that will be demanded by Celtic for the player with QPR who survived relegation the first to place interest in the midfielder.
Mugubi was in the national team that lost 1-0 to Namibia in their second World Cup qualifier in Windhoek on Saturday in a result that placed their Brazil 2014 dreams in jeopardy.
“Wanyama, who played for his country last night as they lost 1-0 to Namibia in a World Cup qualifier, told friends on Friday he wants to quit Celtic and move to the Premiership,” the publication added.
New Liverpool boss Brendan Rodgers has Wanyama on his list of potential summer signings with the midfield area is key to his rebuilding plans at Anfield.
The report adds QPR will try to offload volatile captain Joey Barton to fund a bumper bid for the Hoops favourite.
Stoke will also register an official interest as their manager Tony Pulis is an admirer of the powerful and combative Kenyan.
Celtic are unhappy that news of Wanyama’s desires have been made public and will do all they can to hold onto who they see as a pivotal part of future plans.
If the reports are accurate, Mugubi stands to be the most expensive footballer in Kenyan history and the first to play in the EPL.
His elder brother, McDonald Mariga almost sealed a deadline transfer window move to champions Manchester City two seasons ago.
Mugubi moved to Celtic from Belgian side Germinal Beerschot in a 1 million pound (Sh132m) deal last year.
The Scottish league titleholders then won their case for Mugubi to be awarded a work permit following an appeal to the Scottish Football Association that was then rubber-stamped by the UK Border Agency since Kenya falls outside the FIFA top 70.