The Hoops breathed fresh life into their European campaign with a hard-fought 2-1 win against RB Leipzig in Glasgow earlier this month.
With qualification for the knockout stages hanging in the balance, Brendan Rodgers' men will be targeting all three points when they travel to Norway.
Rosenborg remain pointless after their first four group games and bet365 go 18/5 (4.60) that the hosts restore some pride by beating the Scottish champions.
Celtic are chalked up as a 7/10 (1.70) chance to secure a vital victory.
The most recent match between these teams on Norwegian soil - in Champions League qualifying earlier this season - ended goalless and bet365 offer 14/5 (3.80) that the sides again cannot be separated on this occasion.
Nicklas Bendtner is available for Rosenborg despite his off-field troubles and, indeed, the Norwegian champions should be at full-strength for this tie.
Nir Bitton, Craig Gordon, Eboue Kouassi and Daniel Arzani are all out for the Hoops but captain Scott Brown is in contention to return for the Scottish champions after absence through injury.
Another tight tussle?
These teams have met five times inside the last 18 months and there have been goals at both ends on just one occasion.
The 21/20 (2.05) quote from bet365 for either side to fail to find the target could prove popular with punters, while the same firm go 11/10 (2.10) that there are fewer than three goals scored - that selection would have landed in four of those previous five fixtures.
Rosenborg have scored in nine of their last 10 Europa League ties on home soil, while more than two goals have been scored in seven of the last nine home games that the Norwegian champions have played in this competition.
Ominously for home supporters, though, is the fact that Rosenborg have kept just one clean sheet in their last 14 Europa League ties in Trondheim. Value, then, could lie in backing more than two goals - and both teams to score - at 21/20 (2.05) with bet365.
Odds correct at time of writing. Please gamble responsibly.