Former Scotland international Commons netted an incredible 32 goals for the Scottish champions and Mulgrew believes the 30-year-old can score just as many under new manager Ronny Deila.
But Commons, in Austria with the rest of the Scottish champions' squad for the first day of their summer training camp, has his doubts.
Scotland's double player of the year award winner told the club's television channel: "It's going to be really difficult to reach the goal levels that I did last season.
"But with a new manager coming in with new ideas, it's important to cement your place in the starting XI and that's what lads will be doing in pre-season, try to make it as hard as possible for him to leave you out.
"As far as trying to get to 32 goals again, well that will be very difficult.
"But hopefully I will be in the same sort of areas as I was last year and get on the end of a few things."
Mulgrew, however, believes the former Stoke, Nottingham Forest and Derby attacker will be targeting another haul of goals.
"The amount of goals, important goals, that Kris scored was brilliant for us," he said. "He won us a lot of games.
"I'm sure he will be really happy with it but knowing the type of guy Kris is and the type of player he is, he will want to do even better again and score even more goals."
Celtic will face FC Krasnodar, Rapid Vienna, LASK Linz and Dukla Prague in friendly action before flying to Iceland for the first leg of their Champions League second qualifying round tie with KR Reykjavik on July 15.
And Commons added: "I didn't really pay too much attention to the draw. It is full of teams you have never heard of and have never seen play. You don't know the history that goes with them.
"You just know it is a game that is must-win.
"All our preparations are about getting into that second play-off game and hopefully we can get a decent draw. We need to put this club back where it belongs, the Champions League, and that's all we are thinking about."