Moussa Dembele missed training on Tuesday with a hamstring complaint and will be assessed.
Leigh Griffiths is serving a one-game ban for "provoking supporters" in the previous round against Linfield.
Erik Sviatchenko is carrying a knock, while fellow central defender Dedryck Boyata is a long-term absentee.
Norway winger Pal Andre Helland is Rosenborg's only injury absentee.
Celtic manager Brendan Rodgers said Sviatchenko "could well miss this game" and suggested that 19-year-old Kristoffer Ajer, who spent last season on loan to Kilmarnock, "could potentially" come into contention.
Revealing that Dembele could also be a doubtful starter, he said: "We are looking at a possible injury he may have.
"We could be without him and Leigh, so we need to find a way.
"We do what we always do - we will try to find a solution within the team to make it work."
Even if Celtic have to face Rosenborg without their two leading forwards, history is in their favour.
The Glasgow club have played 25 Champions League qualifying matches at home and lost only four, winning 19 of them.
Celtic have met Rosenborg twice before in European competition, winning three of the four legs against the Norwegians.
Rosenborg progressed to the third round of qualifying thanks to an extra-time win over Dundalk.
The team from Trondheim are top of the Norwegian Eliteserien, 17 games into the campaign, having won the last two championships following five years without winning the trophy.
It is 10 years, though, since they last featured in the group stage of the Champions League.
"We expect a tough game," added Rodgers. "They are well into their season, so they will be at a good level of fitness.
"Rosenborg are very set on how they play. They like to build from behind in a 4-3-3.
"They have good players but are very much based around the strength of the team."
Matthias Vilhjalmsson is pushing for a starting place after scoring the extra-time winner in their 3-2 aggregate win over Dundalk.
However, Rosenborg coach Kare Ingebrigtsen preferred former Arsenal striker Nicklas Bendtner up front for both legs, which meant the Iceland international was in midfield for the first leg in Ireland and on the bench for the return.
Rosenborg captain Mike Jensen is expecting an early onslaught at Celtic Park by a side he rates as favourites to progress to the play-off stage.
"It's a big challenge for us," said Bendtner's fellow Dane. "They are maybe the best team we have played for a long time, but we need to focus on ourselves.
"Everyone will agree that they are the favourites to go through, but the best version of Rosenborg will beat the second best version of Celtic.
"We will have chances and I hope we have the courage to take them. We will have a go. It's not in our style to defend deep for 90 minutes.
"They will come out with a lot of energy and we need to handle that early pressure."
Celtic may be without their two main strikers for the Champions League qualifier against Rosenborg in Glasgow on Wednesday.