Robbie Keane, Matthew Kilgallon and Belarus defender Dmitry Verkhovtsov have been linked with the Parkhead club in recent weeks.

However Mowbray is unwilling to discuss potential targets and knows there are no guarantees he will be able to bring the players he wants to Celtic, although he has already managed to sign South Korean midfielder Ki Sung Yueng.

The former Hibernian and West Brom boss said: "I don't think it is appropriate to talk about individual players. I'm not sure how those names come around.

"I have never heard of some of them, some we are very aware of and some I know are not possible.

"But I don't think you should discuss individuals.

"What we hope to do in January is to add players to help the squad and to help the existing players and not necessarily replace them.

"We have been working very hard in the last few months to identify footballers and areas of the team which needs strengthening and that continues.

"But there are no guarantees that we will bring in anyone other than Ki."

Meanwhile Mowbray has played down the importance of the forthcoming Old Firm game to Celtic's Clydesdale Bank Premier League title hopes.

Celtic are four points behind Rangers, with both sides having two games each before their January 3 meeting at Parkhead.

The Hoops welcome Hamilton on Boxing Day, then travel to Kilmarnock, before the visit of the Ibrox men, who will take on Hibernian and Dundee United.

"For us, the Old Firm game is just another three points to keep our total running," Mowbray said.

"It would be nice to go top and we want to be top from start to finish but that's not the case, it tends to change hands.

"It has been an interesting week. By the time we finished beating Motherwell we were five points clear but by the time we finished our next game against Hearts we were four behind.

"That's the swings and roundabouts you can get at the moment when the games come at different times.

"It would be nice to go into the Old Firm game in a positive frame of mind having won a couple of games and knowing that if we did win that match it would give us the opportunity (to go top).

"But I don't think January 3 is of much significance in terms of where things are going to be in May.

"Rangers have some big games coming up and they will be looking to take maximum points as always, so we will see.

"We are just looking back to get back to winning ways as quickly as possible."

Ki, 20, who will officially join Celtic on January 1, all but ruled himself out of making an Old Firm debut due to lack of fitness.

Mowbray said: "If he is not ready then we will find the right opportunity for him to start his Celtic career."