Brendan Rodgers' side have reached the group stages of the competition in both of the last two seasons and matching that run is the Hoops' minimum target.
Celtic have enjoyed 7-0 and 4-1 wins in their most recent friendly fixtures this summer, against Shamrock Rovers and Standard Liege respectively, as well as their victory in the first leg of this tie.
Alashkert were comprehensively beaten last week and Varuzhan Sukiasyan's side are available at a chunky 20/1 (21.0) with bet365 to claim victory on Scottish soil.
Mikael Lustig, Christian Gamboa, Tom Rogic and Dedryck Boyata are all likely to be rested following their involvement in the World Cup this summer.
Record signing Odsonne Edouard who broke the deadlock in the first leg of this tie, is expected to spearhead the Celtic attack once more, while Scott Bain could deputise in goal if Craig Gordon is not deemed fit to play.
The Hoops led at both half-time and full-time last week and bet365 offer just 4/11 (1.36) that Rodgers' side repeat that feat here, while the same firm go 2/5 (1.40) that the Scottish champions win to nil.
In their first competitive outing of the season in front of their home supporters, the Hoops will be keen to put on a show.
Therefore, it is the 8/5 (2.60) quote for Celtic (-3) to beat the handicap mark that could offer best value for punters ahead of Wednesday's Champions League qualifier in Glasgow.
Odds correct at time of writing. Please gamble responsibly.