Former captain Paul McStay expects Celtic's disappointing recent record in Europe to be at the centre of any end-of-season review.
McStay, 51, deftly avoided criticising manager Ronny Deila but did say that decisions on the club's strategy should be made at the end of the season.
"There's a league to be won and we're on schedule to do that," he said.
"If you come out now and do something drastic it might have some detrimental effect on the team."
Deila's future has been the centre of much speculation since Sunday's Scottish Cup semi-final defeat to Rangers.
It was the third consecutive semi-final loss for the Norwegian, who has failed to progress through Champions League qualifying in his two seasons at Celtic Park.
"European football is what it's all about just now and a massive organisation like Celtic will want to make sure they have things in place for a strong challenge next year," said McStay.
|Celtic in Europe under Deila - 2014-15 (left) & 2015-16 (right)|
|Champ League qual rounds:||Champ League qual rounds:|
|Beat KR Reykjavik (Ice) 5-0 on agg||Beat Stjarnan (Ice) 6-1 on agg|
|Lost to Legia Warsaw (Pol) 6-1 on agg (*awarded tie after Legia fielded ineligible player)||Beat Qarabag (Azer) 1-0 on agg|
|Lost to Maribor (Slov) 2-1 on agg||Lost to Malmo (Swe) 4-3 on agg|
|Finished 2nd in Europa League group to qualify (W 2 D 2 L 2)||Finished bottom of Europa League group (W 0 D 3 L 3)|
|Lost to Inter Milan (Ita) 4-3 on agg in last 16|
No sympathy for Deila
The former Scotland midfielder, who played more than 500 games for Celtic between 1981 and 1997, did stress that he does not feel any sympathy for the under-pressure manager.
"I don't feel sorry for Ronny from the point of view that he is managing one of the biggest clubs in the world," he said.
"Ronny will have been delighted to have been given that opportunity.
"He has given it his best shot and he will continue to do that I think between now and the end of the season.
"I or any coach would love to have had an opportunity like that, so I think he should enjoy it and try to achieve the best he can. That means winning the league."
Deila is on course for a second successive league title, with Celtic enjoying an eight-point lead over Aberdeen going into the last five fixtures.
"I've never met Ronny but I've got a lot of respect for the guy," said McStay. "He comes across as a really good person.
"Right now he's still in a job so I would just leave it at that and allow him to go and hopefully win his second championship."