The Scottish Premiership side are potentially three games away from that stage of the competition.
Luis Suarez during his time with Liverpool
Luis Suarez believes that former Liverpool teammate and Celtic summer signing Kolo Toure is an excellent addition to Brendan Rodgers' squad and will be an important player for them if they reach the group-stages of the Champions League, The Scottish Sun reports.
The 35-year-old - who The Scottish Sun reports will not feature against Barcelona in the Champions Cup clash on Saturday - has moved to Parkhead on a one-year deal (via Mirror).
And despite his age and the length of his contract suggesting that his career is in decline, Suarez - who played alongside the veteran at Anfield during the campaign where they came desperately close to clinching the Premier League title - has insisted that Toure still has a huge amount to offer the Hoops.
"Kolo is a great signing for Celtic. He has so much experience playing at the top level for Liverpool, Manchester City, and Arsenal," he told The Scottish Sun.
"He knows what it is like to play in the big games, in the big stadiums, and if Celtic can progress into the Champions League, he's going to be a very important player."
With the number of injuries within the Celtic squad, it seems likely that Toure will get his chance to prove his value to the team on Wednesday when the Bhoys face Astana in the second-leg of their third qualifying round tie.
And if he is able to take advantage of the fact that several defenders are sidelined with injury by putting in a good performance against the champions of Kazakhstan, then he may find that he has plenty more opportunities to show that he still has a lot to offer even when Rodgers has a fully fit squad to pick from.
Celtic manager Brendan Rodgers