Pukki has made an impressive impact since arriving in Scotland from German club Schalke 04 in a £3million transfer.
The Finnish striker scored on his debut against Hearts at Tynecastle earlier this month after coming off the bench midway through the second half, and he also netted on his first start for the Scottish champions in the 2-1 win over St Johnstone at Parkhead on Saturday.
Yet the 23-year-old knows that, with Anthony Stokes also enjoying a rich vein of form, he is not guaranteed a game against Barca.
Neil Lennon will almost certainly go with a lone hitman in the eagerly-anticipated Group H tie with the Catalan superstars a week today.
And he preferred Stokes up front in his team's Champions League opener against AC Milan in Italy last week.
But Pukki is hoping he can play his way into the starting line-up in the League Cup tie with Morton and the SPFL Premiership game with Kilmarnock at Rugby Park on Saturday.
He said "It's important to keep our concentration on this game and get the result. The League Cup is very important to us and we want to win it.
"There is still one week to the Barca game, and we have one league game before that as well, so we have to concentrate on the game that is in front of us.
"But of course I want to play in those games against Barca. To be in the team would be like a dream.
"I have to work hard in the games and I hope I can prove myself to the manager."
Pukki, who came on against Milan towards the end of the game over in the San Siro, has been rightly pleased with how the start to his Celtic career has gone.
In particular, he has been happy with the understanding he has quickly developed with Irish forward Stokes in his first-team outings so far.
However, the Finnish internationalist, who was not a regular starter at Schalke, is refusing to get carried away with his success to date and stressed he will continue to work hard on his game.
He stated: "It's been a great start for me and I hope I can keep it going. I really enjoyed my first game at Celtic Park.
"It's a nice stadium with a good atmosphere and I got my first goal there. It's always important for a striker to get going as quickly as they can. Now I have scored I can be more confident.
"I don't have to be thinking I have to work hard for my first goal. Now I can play more. I can play without that pressure, which is good.
"I haven't been thinking of how many goals I could score. I just want to help the team. I hope to score many goals, but I haven't put any limit on it."
Pukki continued: "I think Anthony and I have played well together. He has assisted both my goals, so it has been good to play with him.
"At my age it is important to play and develop. I really wanted to go somewhere I could be more part of the team and where the coach really trusts me.
"At Schalke, it wasn't really like that. I got the feeling that the manager really wanted me here. After that, it is up to me and how I play. Of course, I still need to work hard to keep playing more and more.
"The games haven't been so easy for us, but I knew they would be physical. But I played in Germany, which is quite a physical league so it is no problem.
"The tempo is about the same here, but the Bundesliga is one of the best leagues in the world so I don't think it will be anything new for me to play here.
"I am a more of a technical player, so what I have to develop more is the physical side of my game.
"It would be great to be a hero of the fans. I just need to keep working and I hope I can score a lot of goals."
Pukki spent time at Schalke with Dutch striker Klaas-Jan Huntelaar and Spanish star Raul and believes working alongside them helped to make him a better player.
He reflected: "Huntelaar is one of the best goalscorers in the world and you can learn from him just from watching him in training and in games.
"I also played with Raul, who is another good striker to learn from."
Pukki confessed he had never heard of SPFL Championship club Morton - other than his countrymen Janne Lindberg and Marko Rajamaki having played for them in the 1990s.
He said: "I know of Lindberg and Rajamaki. They are both coaches in Finland. We will treat Morton with the utmost respect and work hard to get the result that will put us into the next round."