The Swede, who became Neil Lennon’s number two in 2010, confirmed last week that he is leave the Parkhead club when the current campaign ends to “seek some different opportunities”.
With four games remaining in the Scottish Premiership, the first of which is against Inverness at Celtic Park on Sunday, the Hoops sit on 89 points and the Scotland international believes reaching the ton would be a fitting farewell for Mjallby.
“That would be great, that would be the aim,” said Mulgrew.
“We’ll just need to do our best to win all the games but we will take each game as it comes and hope to win that first.
“Inverness have been good this season. They are always tough and strong and I’m sure they will be ready for it on Sunday again.”
Mulgrew paid tribute to the influence Mjallby, a former Hoops defender, has had on him and the rest of the Celtic players in the past four years.
“He had a big influence on me when I first played at centre-half after not having played a lot of football there in my career,” said the 28-year-old utility player.
“He was such a great centre-half himself so he was a big help and passed on his advice.
“And he’s always involved. He’s always at the training pitch taking sessions and passing on his ideas, especially to the defenders.
“It’s disappointing (that he’s leaving) but I’m sure he thought long and hard about it and it’s the best decision for him.
“It’s a big job, and whoever comes in will have a big role to play.
“But I’m sure the manager will pick the person for the job and I’m sure he’ll be ready to come in and help us out.”
Celtic have drawn two of their last three games since clinching their third successive title against Partick Thistle at Firhill but Mulgrew, who returns after recovering from a hamstring injury, insists there will be no problems getting motivated for Sunday.
“Just playing for Celtic should be enough to give you the motivation,” said the former Wolves and Aberdeen player.
“The fans demand it, the manager pushes us every day and that should be enough to keep us motivated and ready to go come Sunday.
“It’s been a good season. We’ve qualified for the Champions League (for next season) after getting to the last-16 the year before this one.
“Maybe the expectation was there a bit more it this year but it was always going to be a hard group to get out of.
“The domestic cup competitions could have been better but the way we won the league and form we showed has been great so, overall, it’s been a good season.”