While boss Neil Lennon is not prepared to identify his target, he did confirm the Parkhead club have set the ball rolling.
He is delighted the 1-0 victory over St Johnstone has pushed his still-unbeaten side 11 points clear in the Premiership before the halfway point.
But Lennon is not backing off in his quest to bring in another goalscorer and a creative player.
"We have made strides in trying to get one player in," said Lennon. "We are in talks, but nothing is confirmed yet."
The South Korean defensive midfielder, Han Kook-Young, who currently plays for Japanese club, Shonan Bellmare, claims he has already been approached by Celtic.
Al-Ahly's 19-year-old Egyptian playmaker, Mahmoud Hassan, is another name linked with the Scottish champions, while the club had Japanese attacking midfielder, Hiroki Yamada, on trial at Lennoxtown last week.
Strikers Alfred Finnbogason from Heerenveen and Aron Johannsson from AZ Alkmaar are also on the list of players put under the microscope.
But, to keep options open, scouts were also deployed this week down south running the rule over strikers in the hope the man can be identified and secured to convert the many chances the Hoops are creating.
Pre-contract agreement hitman, Holmbert Finjonsson, will be eligible to start playing for the club from Wednesday, when Partick Thistle come to Parkhead.
But the Icelandic youngster will only be the first of the new arrivals, if Lennon has his way.
He wants them in as quickly as possible, with the club flying to Turkey for a mid-season training camp and tournament after they play St Mirren a week on Sunday.
Lennon believes it is essential they bolster a squad which is the envy of every other manager in the country, but which he considers is in real need of strengthening.
He said: "People think we have a relatively strong squad. But we don't. A few injuries, and we are looking pretty thin at times.
"The likes of Scott Brown, Virgil van Dijk, Efe Ambrose, Kris Commons and Fraser Forster have played a huge volume of games - basically a season in half a season for a lot of players.
"A lot of these matches have been high-intensity, pressure games, but I don't want the players to tail off now.
"Hopefully we can get into the break we are taking next month unbeaten, and come back even fresher for the second part of the season."
That ambition will be easier to realise when the new signings arrive, and when some of the injured stars already at the club return to action.
Charlie Mulgrew is one in particular Lennon wants to see back in the side, and he said: "Charlie is a good player, and he will make us better.
"We're also hoping to get a run of games out of James Forrest.
"If he can just manage to avoid the constant niggling injuries, then he makes us better, too."