Celtic chairman Brian Quinn is confident striker John Hartson will agree new terms with the club.
The Wales international is now free to speak to other clubs, with his existing deal with the Hoops due to expire at the end of the season.
However, Celtic manager Martin O'Neill and Hartson's agent Jonathan Barnett were encouraged by the latest round of talks during the week and Quinn now expects a quick conclusion.
Quinn told BBC Radio Five Live: "I don't think that a move will happen.
"I'm pretty confident that John Hartson will be staying at Celtic, not just this season but for one or two more seasons to come.
"Negotiations are very well advanced and they are advanced in a direction that makes me confident that those Celtic fans nervous about John Hartson can relax."
Quinn is also optimistic of retaining the services of highly-rated manager O'Neill and believes there are enough challenges lying ahead to keep the Northern Irishman in Glasgow.
"I don't think he has gone as far as he can," the chairman added.
"There is a need for us to look at the strength of the team in relation to those teams in the Champions League and we will never be able to match them.
"That's something you have to consent. Those teams have massive resources compared to Celtic.
"But we have got a manager who is able to counteract that to some extent. He is very smart and he is at his best in European games and I think he can take us further.
"I am always hopeful rather than say confident that Martin will be given a challenge at Celtic that will keep him with us."