The former Liverpool and Swansea City boss has taken over from Ronny Deila.
"We can't wait to get in and see how he wants the team set up and how he wants us to play," Gordon told BBC Scotland.
"That's the most exciting part of it - going into pre-season. Normally, you dread going back in, thinking it is going to be hard work."
Celtic's close season is a short one as their new campaign starts with the second qualifying round of the Champions League on 12 or 13 July.
And, after chatting to staff at Celtic Park on Monday as fans queued to buy season tickets, Gordon came away with the impression that the choice of Rodgers has enthused others around the club.
"It is a massive appointment and a huge name with a great track record coming in," he said of Rodgers, who was greeted by 13,000 fans when he was presented as the manager.
"For me personally, it is very exciting and I think the rest of the players are of the same mindset.
"We are looking forward to getting down to the hard work and seeing what we can do this season."
Gordon was not surprised that Celtic - who have won five Scottish titles in a row - have been able to attract such a high-profile manager because of "the potential it has in Europe and the worldwide appeal that Celtic has".
"I can totally understand why Celtic went for a big name and why someone would want to come to Celtic as well - if somebody is willing to put footballing reasons above everything else," said the 33-year-old Scotland international.
City rivals Rangers return to the top flight after winning promotion and they, along with Hearts and Celtic, are reporting healthy season ticket sales.
"It looks like it's going to be a good league with some big teams who are capable of beating each other at the top end of the league, which is perhaps something we've not had in recent seasons," added Gordon.
"Obviously, with Hearts coming back up there and doing pretty well and capable of taking points off the other teams in the top six, there's potential there for teams to drop points.
"That's what makes it exciting for everybody to watch and also to play in as well."