Japan international Shunsuke Nakamura was involved in the Asian Cup this summer and will not report back to Celtic Park until Friday.
New signing Scott McDonald, who has impressed in pre-season after signing from Motherwell, is suspended for the first two SPL games of the season.
And goalkeeper Artur Boruc could even miss the start of Celtic's Champions League campaign on August 14 with a troublesome shoulder injury picked up during the friendly against Newcastle at St James' Park last Thursday.
All three players missed the 1-0 friendly win over Parma at Celtic Park yesterday which the Hoops won with Aiden McGeady's goal in the 84th minute.
Burns said: "Shunsuke does not come back until Friday and he will need to speak to the manager.
"Artur has got a problem with a joint in his shoulder which he picked up 10 minutes into the Newcastle game. He could be out for two or three weeks.
"We will do everything that we can to be fit but we've got to be careful or we could make it worse.
"Scott McDonald is suspended for the first two games of the season but whoever comes in, it will be up to them to keep the jersey."
Second-choice goalkeeper Mark Brown, who has been waiting patiently in the wings since signing from Inverness Caledonian Thistle last January, deputised against the Serie A side and will keep his place for the Kilmarnock match.
And the former Rangers and Motherwell stopper is set to take over in the first leg of the Champions League third qualifier, which will be drawn on Friday.
Burns admitted Boruc is struggling to be fit for Europe.
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