St Johnstone have completed the signing of former Scotland striker James McFadden after a successful trial.
Cheick Tiote has revealed his desire to leave Newcastle and admits he has previously been contacted by Arsenal.
Celtic chief executive Peter Lawwell has reassured fans the club will seek to ensure continuity despite some players "inevitably" looking to move on in the summer.
Manager Neil Lennon admitted it would be difficult to keep his squad together following their run to the last 16 of the Champions League, after their European adventure ended with a 2-0 defeat by Juventus in Turin on Wednesday night.
The key players who are most expected to move on are versatile midfielder Victor Wanyama and striker Gary Hooper, who attracted several bids from Norwich in January and is approaching the final year of his contract.
But Lawwell is keen to ensure that Lennon can hit the ground running when Celtic's next Champions League campaign begins.
As such, he does not look like sanctioning widespread departures - and promised to provide adequate replacements for those that do leave.
Lawwell told Sky Sports News: "I think inevitably there will be one or two players that will probably want to move on.
"But stability is a very important thing in football so we would hope to get the balance right, to make sure that there is some quality coming in that may replace those that are going, but keeping a real balance in terms of stability and continuity going into, hopefully, the qualifiers next July."
Lawwell also recognised that his manager's stock has risen from their run to the knockout stages, despite a 5-0 aggregate defeat by a clinical Juve side.
Lawwell said: "It's been a great season so far. The Champions League has been wonderful - wonderful for Celtic and wonderful for the players and for Neil.
"Clearly, we are not naive enough to think that people won't be recognising that elsewhere.
"If he keeps progressing and being successful, I'm sure he will be courted at some point.
"But Celtic is a big part of Neil Lennon and maybe he won't be able to get elsewhere what he gets here at Celtic.
"We are hoping that he stays for a long, long time."
Celtic's European run began with qualifying victories over HJK Helsinki and Helsingborgs and progressed beyond anyone's realistic expectations.
Lennon's team went to Spartak Moscow and secured Celtic's first away win in the Champions League proper. They came within seconds of gaining a point in the Nou Camp before stunning Barcelona with a 2-1 victory at Celtic Park.
And they kept their nerve to qualify for the knockout stages with victory over Spartak in an anxious final group game before pushing Juventus at Parkhead following an early setback.
Lawwell said: "It was a long haul going into the qualifiers. To a great extent we were going into the unknown, it was a new young team that hadn't been tried at that level.
"They performed magnificently - they took on Europe's best and performed at a very, very high level."