It might be prudent for Arsenal to make a January bid and jump the queue of clubs that are interested in Wanyama. Manchester United have been linked with the Kenyan, while The Independent's story also names Real Madrid as known admirers of the player.
The 21-year-old Wanyama made headlines this season when he scored in Celtic's 2-1 Champions League victory over Barcelona, but it's fair to say that the player was already on a few shopping lists before that goal.
In the summer of 2011, Celtic bought Wanyama for £900,000 from Beerschot AC of Belgium, fighting off interest from CSKA Moscow. The defensive midfielder quickly established himself in the first team, featuring in 42 games in his debut season in Scotland and displaying his versatility, making appearances as a centre-back and full-back.
Given his size, it's no surprise that Wanyama can do a turn in defence and he would certainly add some physicality to an Arsenal midfield than can sometimes be overpowered. Wanyama is 6'2" and yet even at this height, still cuts a stocky figure. He's very strong, fast for his size and can run all day.
A fearsome tackler, Wanyama also possesses the type of close control and neat passing required of the modern defensive midfielder. He's also pretty handy going forward and is perfectly capable of developing into a box-to-box type player.
Wanyama certainly has the physical capabilities to become a driving force in the midfield, in the style of Yaya Toure or indeed, the Arsenal legend Patrick Vieira. He's also a very dangerous finisher anywhere around the box. Wanyama has already scored seven goals this season and has hit some spectacular long-range strikes during his brief Celtic career.
If you were going to raise a question mark about the player, his disciplinary record would come under scrutiny. Wanyama was twice hit with suspensions while in Belgium (one for an off-the-ball elbow) and was sent off against Rangers last season.
Given Wanyama's age and the position he plays, he can surely be forgiven for getting into a few scrapes. Naivety is to be expected in one so young and you would hope that he learns from his mistakes, rather than becoming a walking yellow-card-magnet like Cheick Tiote.
The Celtic manager Neil Lennon has valued Wanyama at £25m. I think that we can take that estimation with a pinch of salt, but with his contract not due to expire until 2015, he won't be cheap either. Somewhere in the region of £10m to £15m would likely be enough to tempt Celtic to sell.
So will Arsenal take the plunge? If they don't move now, they might find themselves in a bidding war come the summer, against the type of club that they would struggle to compete with financially. It's now or never Arsene.
Do you think that Arsenal should buy Victor Wanyama?