The draw for the first knockout stage will be made on Thursday and the Israeli international midfielder said: "We believe we can win against anyone".
Celtic will face one of the group winners; Paris Saint-Germain, FC Schalke 04, Malaga, Borussia Dortmund, Juventus, Bayern Munich or Manchester United, in a tie that will be played in February and March.
"I think Malaga would be a brilliant draw for us," added Kayal. "We want to believe we can win against anyone, because we are professionals. We are playing on a higher level now. There is no-one we want to avoid in the draw. We are still hungry to prove a lot in Europe. Two months ago, no-one believed we could make it to the last 16."
The 24-year-old, who signed for Celtic from Maccabi Haifa in 2010, believes that Neil Lennon, the Celtic manager, had "changed the mentality of the players", thus paving the ways for victories over Barcelona and Spartak Moscow that led to the Parkhead side denying Benfica for the second qualifying spot in the group.
"It's a young squad – nobody wants to stop now," said Kayal. "We're looking forward to more success and to taking the team forward. We don't think the last 16 is the maximum possible for this team. I don't agree with those who say it is. Maybe we can surprise them again."
Kayal was speaking in the aftermath of a 2-0 victory over St Mirren which took Celtic four points clear at the top of the Clydesdale Bank Premier League with a game in hand. The easy win ended a run of underachievement in the SPL at Celtic Park as the champions had not won on league duty since October 7.
"I think we are in a good position now and it is possible we can have a big advantage at the top of the SPL by the time the next Champions League game comes around," added Kayal."
Seeded group winners will be away in the round of 16 first legs on February 12/13 and February 19/20 and at home in the return matches on March 5/6 and March 12/13.
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