Celtic manager Neil Lennon concedes some players may exit in the summer, but any replacements to his squad will rely on future income.
Following the title win against Inverness at Celtic Park, Lennon insisted he has a solid core of players but will seek to make improvements.
"I'm pretty sure we'll lose a player or two," said Lennon. "We've got the core.
"It depends on what money we take in and where we can improve, but we're working away on that for the summer."
Celtic claimed their 44th league title, the second successive championship win in a row during Lennon's tenure, with a 4-1 win against Inverness Caledonian Thistle.
The four goals to claim the crown arrived during a 20-minute period in the second half, two from the boot of Gary Hooper, and Lennon admitted it was a terrific experience for the players and the club's supporters to claim yet another honour in their 125-year history.
"These days don't come round very often," said Lennon. "This is the eighth title I've been involved in, but to do it as a manager back-to-back is pretty special for me as an individual.
"Sometimes the players don't get the credit that's due to them, but winning the title is a very difficult thing to do.
"Everyone wants to beat you and have a piece of you. I think what gets overlooked is how young the team is.
"Winning the title last year made me a bit more comfortable, if you can ever get comfortable in the role. It made me more comfortable this season, and obviously the European campaign was a huge part of our season."
"There's no real veterans or experience players in the team. They've got so much in front of them, but the way they handle the pressure and play with the style that's pleasing on the eye."
Following the final whistle, goal-hero Gary Hooper was asked on television if he would still be a Celtic player next season and replied "we'll see", but his manager remains confident that there is a still a chance of keeping him.
"I have made my submissions to the board regarding Gary," said Lennon.
"I haven't really spoken to his agent lately at length but I would like to keep Gary here because he is such an important player.
"Goalscorers are at a premium, he is only 24 and has got 28 goals this season, 18 in the league. He is two short of having 20-plus goals in the league for the third consecutive season which shows what an important, pivotal player he has been.
"We don't want to break the wage structure because one thing that is important is team spirit.
"These players, who are not on huge money, have raised the bar here over the last couple of years but we will do what we can to keep him."
Given the precarious financial position of Scottish football and the turmoil that has engulfed plans for league restructuring, Lennon also indicated that the club would have to adopt a cautious approach towards transfers over the coming months, but insisted he was keen to build on the current crop of players.
"I believe the squad needs improvement in terms of where we want to take it, in specific positions," said Lennon.
"We've always worked with money that's come in - we've used it and spent it prudently no the squad.
"I would like a little bit more experience around my players with some quality that will make us better."
Up next for Celtic is the remaining fixtures in the SPL before being presented the trophy at home to St Johnstone on 11 May, then the Scottish Cup Final against Hibernian on Sunday 26 May at Hampden.
A win for Celtic against the Edinburgh side would earn Celtic the league and cup double.
Lennon added: "If I could achieve the double as a manager, that would rank right up there with anything I've done."