No approaches have been made for the 21-year-old but Mark Hughes, the new Stoke manager, is a known admirer of the Kenyan internationalist and is reportedly considering an offer of almost £10m to take him to England.
Although both Internazionale and Arsenal have been recently linked with Wanyama, it is the interest from Stoke which is being most closely monitored within Parkhead and is seen by senior club sources as the most credible at the moment. Any bid of around £10m for Wanyama would prove impossible to resist for a player Celtic paid only £900,000 to sign from Beerschot, in Belgium, in 2011.
Gary Hooper and Fraser Forster have also attracted interest from Barclays Premier League clubs, but it is Wanyama – currently back in Kenya preparing for a World Cup qualifier against Nigeria this week – who could be the first to attract serious money.
Last night, Arsenal midfielder Aaron Ramsey, speaking in Kenya to promote the country's tourism trade, was asked about the prospect of Wanyama moving to The Emirates and said: "If Arsenal get to sign Victor Wanyama I will be the first to welcome him. I have watched him play for Celtic, I watched him score against Barcelona and I think he is a great player. Whether he will join us is for other people to decide.
"He is one player many clubs in England are chasing and I have no doubt he has great talent if top clubs in England are interested in him. For a Kenyan to win the young player of the year award in Scotland, it means a lot."
Manager Neil Lennon met Dermot Desmond, Celtic's majority shareholder, and Peter Lawwell, the chief executive, last week to discuss this summer's transfer budget and his own contract. Celtic are not likely to make any imminent transfer market moves and expect to wait until later in the close season before adding to the squad which won the double and reached the Champions League last 16. Striker Yannick Sagbo, 25, and full-back Brice Dja Djedje, 22, two Ivorians at the French club Evian and available for around £2.5m each, were watched by Lennon in Friday's French Cup final and are on a list of potential transfer targets.
A striker is a priority and Amido Balde, the 22-year-old Vitoria Guimaraes forward, is also being watched, as is Dundee United's Johnny Russell, although Celtic are undecided about making a bid for the 23-year-old and may not submit an offer which betters anything from Derby County.
Although there were weekend reports of interest in the Newcastle United pair, Conor Newton and Paul Dummett, who both had loans at St Mirren last season, neither are on Celtic's list of possible targets.