Peter Lawwell, the chief executive, Neil Lennon, the manager, and the support staff at the club have already started frank discussions that will continue over the summer.
In the absence of transcripts of these talks, it was a small consolation to be allowed a hint of Lennon's thinking in the aftermath of a week where Rangers were demolished and a victory over St Johnstone took Celtic to 90 points in the Clydesdale Bank Premier League. Two wins – against Dundee United on Sunday at Tannadice and against Hearts at home – can take Celtic to the highest total in the league since the 94 points the Parkhead side recorded in 2004.
The accumulation of points is the name of the game, but it is the form and prospects of the players that energises the support. Lennon seems in a strong position in terms of personnel. He did not seek to hide his satisfaction at the performances of his players in recent weeks. Celtic have been lifted by the resurgence of such as Emilio Izaguirre and Kris Commons, who both have missed much of the season through injury.
''They wanted to prove they were the players we know they can be and they have done that,'' said Lennon of the Honduran and the Scottish internationalist. With Biram Kayal returning to full fitness, Lennon has three fresh and motivated players for the new term.
Other players have made their name during the campaign. The most obvious is Victor Wanyama. Lennon can not conceal his admiration for the Kenyan, who has shown power and touch in midfield. Joe Ledley and Scott Brown have been influential in central areas, with Fraser Forster quickly improving in goal.
Lennon, though, was most expansive about Charlie Mulgrew and James Forrest, who have won the football writers' player of the year and the young player of the year respectively. ''James could go on to be a superstar in the game. He has been a real find for us in the last couple of seasons,'' he said of the winger he promoted immediately to the first team squad on taking over as caretaker manager in 2010.
Of Mulgrew, he said: ''Charlie has just developed into a top-class international player. It's not been easy for him, it's been a long road, but he is a great example to all the young players who have been released early in their careers.
''I think Charlie lacked a bit of belief when he came back at first. He had a difficult baptism. He was thrown in to the Champions League at left-back and it was a big step up for him from Aberdeen. But once he found his feet later that season he came knocking on my door one day. He was training very well. He said: 'Look gaffer, can I get a chance?' I told him: 'You'll get your chance soon'. We played him at Ibrox and since then he has never looked back.''
Mulgrew has played at left-back, in midfield and at centre back for Celtic. ''He is just a good all-round quality footballer with a good footballing brain," added Lennon.
The verdicts on Rabiu Ibrahim, 21, and Mo Bangura, 22, will be given after further evidence is provided. Ibrahim has a three-and-half-year deal, which suggests he made an immediate impression when on trial at the turn of the year. He also entertained the supporters on Thursday with a 17-minute cameo that should have included a goal but Gary Hooper, in an offside position, made sure the Nigerian's shot was travelling over the line.
"I was really happy with Ibrahim,'' said Lennon. ''He got a goal taken off him by Gary and I'll be fining Gary for that, but I was very pleased with Ibrahim's contribution. Hopefully we will get him some more game time between now and the end of the season.''
Small, quick and with an eye for a pass, Ibrahim has so far failed to frank the assessments made of him when he was the star member of the Nigerian under-17 team. He undoubtedly has the talent, but his stay in Glasgow will be crucial as to how his career progresses.
Bangura, in contrast, finds it hard to make an entirely favourable impression. He is quick and strong and held the ball up to some effect against St Johnstone, but still can not find his first goal for the club. Lennon, though, was upbeat about his £2.2m signing from AIK. "I was really pleased with Bangura. He has been hampered by a knee injury," said the manager. "While he probably got a bit tired towards the end, it was understandable. But he looked really fresh and his link-up play was good, particularly in the first half. He deserved a goal. He was unlucky with the one that hit the post. We are hoping to see the best of him next season.''
One player will have no further role in the Celtic story. Mark Wilson, 27, a full-back whose career has been blighted by injury, was captain for the night, though typically he hobbled off after a knock.
Lennon has constructed a squad that means the departure of Wilson, the player, will go almost unnoticed. He will be missed, though, as a man.