The SPL champions had announced the agreement of a 14.5 million euros 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 1.1m euros fee.
Modia blamed the Bhoys, claiming that Wanyama had already lost over 1m euros by not being allowed to join QPR last summer and warning that the 21-year-old would not be pressured into joining a club solely because it suited the Parkhead side.
"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."
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.