The 21-year-old midfielder has attracted interest from a host of Premier League clubs, after turning in a series of impressive performances - both domestically and in Europe - for the Bhoys.
Wanyama became the first Kenyan to appear in the Scottish Premier League when he joined Celtic in 2011 from Belgian side Beerschot, and has garnered more admiring glances after playing an instrumental role in helping Neil Lennon's side through to the knockout phase of the Champions League this year.
Gunners boss Arsene Wenger has identified the holding midfielder as a transfer priority for Arsenal this summer, and plans to lure the Celtic star to the Emirates Stadium at the end of the 2012/13 campaign.
Following the summer sale of Alex Song to Barcelona, Wenger is mindful of having become over reliant on Mikel Arteta in the holding role, although he has been encouraged by Aaron Ramsey's recent performances there.
The frugal Frenchman failed with a deadline-day bid for Toulouse midfielder Etienne Capoue, but is also actively watching other targets and requested a report on Wanyama from Tuesday evening.
However, Arsenal will face competition for the African's signature from Premier League rivals Manchester United, with Sir Alex Ferguson also believed to be monitoring the player's situation, with a view to adding him to his ranks at Old Trafford.
The Red Devils were heavily linked with Wanyama during the January transfer window, and Sky Sports reported that Ferguson himself even made a personal check on him during Celtic's recent 4-0 win over Dundee United, while the Manchester United squad enjoyed a warm-weather training camp in Dubai.