Scouts from both clubs are due to watch the £7m (Sh920.5m)-rated Kenyan play for Celtic in their Champions League qualifier with Helsinki which will be the third time in recent weeks reports the Daily Mail.
Representatives from both clubs also watched him against Norwich and Inter Milan where he impressed in his preferred midfield role.
QPR are also in the running for the 21-year-old with champions Man City and Liverpool other clubs said to be interested with the player who looks set to be the first Kenyan to break into the lucrative English Premiership.
His elder brother, MacDonald Mariga came close top moving to City in the January transfer window two seasons ago before being denied a work permit by the British Home Office due to Kenya’s lowly Fifa ranking at the time.
Mariga went on to join Inter Milan in Italy where he won the treble but having played in the Scottish Premier League last season after moving Swedish side Helsingborg.
Earlier, the desired midfielder stated his intent to play for Celtic this season with his manager, Neil Lennon stating the Hoops mission to retain his services as they pursue qualification and featuring in the Champions League.
Wanyama is the third Kenyan player to feature at Europe’s elite club football competition after his elder sibling and Harambee Stars captain, Dennis Oliech who featured at the event with French club AJ Auxerre before their relegation.
Meanwhile adds AFP, Celtic defender Charlie Mulgrew says the demise of rivals Rangers means it is more important than ever that the club qualify for the Champions League group stages.
The Hoops player and his teammates are preparing for a crunch tie against HJK Helsinki in the third qualifying round at Parkhead on Wednesday as they bid to make the money-spinning group stages of the competition for the first time since 2008.
Twice in recent years the Parkhead club have crashed out of the Champions League at the qualifying stage after coming unstuck against Arsenal and Braga while also losing out on a spot in the Europa League to Utrecht and Sion.
The Swiss outfit’s rule-breaking did hand them a Europa League reprieve last year but failure so early in Europe is costly to the club.
And Mulgrew knows that the price of failure against Finnish champions HJK would be even more severe this year — because there will be no Old Firm money to fall back on.
With Rangers banished from the SPL after the club was demoted to the third division when it couldn’t be saved from liquidation, entry into Europe’s elite tournament and the millions that go with it are vital as Celtic bid to make up for the loss in attendance money caused by the absence of their fiercest rivals.