Celtic insist they made every effort to hold on to Jackie McNamara, despite the player's claims Wolves worked harder to sign him.
The Scottish international joined the Molineux club on a two-year-deal on Tuesday, bringing his 10-year spell at Parkhead to an end.
The 31-year-year-old defender - whose final game was his testimonial match against the Republic of Ireland - was expected to extend his stay at Celtic Park, but was disappointed they were only willing to offer a one-year extension.
McNamara verbally agreed the move to Wolves by phone on Tuesday night, but has revealed how the Hoops stepped up their attempts to retain him while he was on his way south for a medical.
The Glasgow giants say they matched the offer of a two-year deal as well as improving the terms, but insist McNamara leaves with their best wishes.
A Celtic spokesman told the club's official website: "Celtic offered Jackie a greatly improved deal and, contrary to reports, we offered Jackie a two-year contract with the club.
"Naturally, we are disappointed that Jackie has chosen not to accept our offer but this is clearly his prerogative to do so.
"We wish Jackie well for the future after the contribution he has made to the club."
