However, the Hoops' boss, speaking through the club's website, said:
"The story is absolute nonsense.
"I never told Scott Brown that I want him to leave the club. Scott is a huge player for Celtic and absolutely part of the future plans of this club.
"I have worked with Scott for a number of years and have a great relationship with him.
"It's disappointing that people are able to write things which are so inaccurate.
"But I know our supporters will understand that unfortunately this is one of the things we need to deal with.
"I am sure they will also know that we are all working together at Celtic to do all we can to achieve success for the club,"
Brown was quoted in the article as saying: "Yes, there was a conversation between myself and the manager but I am not prepared to go into details.
"I believe these things should remain private. Maybe you should ask him what was said. I have nothing more to add."
However, on the club website the Celtic midfielder said: "Obviously I am very disappointed with this article as there is no foundation to it.
"I have worked with the manager for some time and have a very good relationship with him.
"It's disappointing to have been out for so long with an injury but I'm looking forward to getting back to full fitness as soon as possible and getting back in to the team for the second half of the season."
A spokesman for the Parkhead club, who are currently taking legal advice over the issue, added: "As a club, we can only speculate about the motivation of such an erroneous article but we can assure the Celtic supporters that we will not allow this type of reporting to unsettle the club or the player.
"At this stage of the season, it's more important than ever that everyone at Celtic Football Club and the supporters pull together. We will not let this be disrupted by any outside interference."