Swedish full-back Mikael Lustig is already on his way from Rosenborg, and manager Neil Lennon is now waiting to hear if he is to get the green light on other targets.
Dundee United youngster Scott Allan – who is out of contract in the summer – has been strongly linked with a move to Parkhead, although West Brom have already agreed a £400,000 price with the Tannadice club and Rangers remain in the hunt for the Scotland Under-21 star.
But it is Maritimo's Baba Diawara who remains top of Lennon's Christmas wish list, and the Hoops boss checked out the form of the Senegalese striker during a flying visit to Portugal at the weekend.
Celtic had agreed a £2million transfer fee with the Madeira-based club in August, but the deal fell through over work permit issues.
There is now increased competition for 23-year-old Diawara. French club Sochaux are keen on landing him, and this could spark the kind of auction which Celtic had hoped to avoid.
Lennon is also in the market for another defender.
Manchester City boss Roberto Mancini, meanwhile, has confirmed that left-back Wayne Bridge turned down the chance to move to Parkhead on loan in the last transfer window.
He said: "In the summer, Wayne had the chance to play for Celtic, and this is an important team."
When the 31-year-old English international rejected their approach, Celtic tuned to Dynamo Kiev to bring in Badr El Kaddouri. But the Moroccan has struggled to make any impact, and his loan deal is expected to be terminated.
The club have confirmed that Daniel Majstorovic will be out of action for six weeks after undergoing surgery on the cheekbone he broke at Perth on Sunday.
But better news for Lennon is that Emilio Izaguirre and Kelvin Wilson both played for 90 minutes in a bounce game against Morton at Lennoxtown yesterday.
The medical staff will assess if they have suffered any reaction before Lennon decides if they are ready to play against Kilmarnock on Saturday.
Celtic's game at Hearts, scheduled for January 28, has been rearranged for Wednesday, February 8, to accommodate the League Cup semi-final with Falkirk.