The SPL champions had announced the agreement of a £12.5 million fee with the Premier League side but the Kenyan midfielder told Goal that he was not even made aware of the offer, with his agent, Ivan Modia, denying that his client would join the Saints, reportedly because the south-coast club would not pay the representative a £1m fee.
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"These negotiations like any others are carried out by Celtic in a private, proper and professional way," the Scottish club said in a statement.
"Celtic carries out its business with integrity, we work to the highest standards and in the interests of the club, our supporters and indeed our players.
"We do not need to comment any further on this player."
As reported by Goal, Cardiff City, Everton and Liverpool are all interested in taking Wanyama to the Premier League, with the newly promoted side willing to offer a higher salary but lower transfer fee than Southampton.