Neil Lennon dismissed reports that a pre-contract agreement is in place with Ben Davies - but did tease the club could spend if the right deal comes up.
The 25-year-old defender has been heavily linked with a move to Paradise, with one outlet claiming yesterday that a package had been agreed.
Record Sport understands that while Celtic have tabled an offer, the talented Englishman also has offers on the table from two Premier League sides and seven Championship teams.
And Lennon confirmed that no deal has been finalised with the in-demand star.
Asked if an agreement had been signed, he said: "That's not the case.
"When I have something for you I will let you know as soon as possible but there is nothing been done today or yesterday so it's as you were at the minute."
Video: Jurgen Klopp looking for a new defender but knows pursuit will not be easy (Evening Standard)
Jurgen Klopp looking for a new defender but knows pursuit will not be easy
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Pressed on the club's interest in the left-sided central defender, Lennon refused to be drawn further.
He said: "I don't want to talk about speculation on players coming and going until they are signed on the dotted line.
"That's always been our way and we'd like to keep it that way."
With Jeremie Frimpong having been sold to Bayer Leverkusen and Christopher Jullien on the treatment table once again, there is cause for concern over defensive strength in depth.
And Lennon admits that fortifying that department will be a priority in the window's remaining days and that the club could even splash some cash on replacements.
He said: "Obviously Jeremie is gone and Christopher is out for a considerable length of time.
"So we are looking for one or two replacements in that area.
"You never know. If a deal comes up that we like there may be funds available to do that."