The likes of Gary Hooper, Victor Wanyama and Fraser Forster have all been linked with other clubs but Mulgrew hopes they stay put as the Hoops prepare for Juventus in the Champions League Round of 16 first leg next month.
"You can't worry. If it happens, it happens," he told SunSport.
"But there is a lot to play for at Celtic.
"We're in the last 16 of the Champions League, so it's a choice for every player to make. We'll see what happens.
"It's good news if the big players stay here, but who knows what will happen.
"Hopefully, we can keep the team together.
"This is a young team growing and I believe we can go onto better things.
"I know people can be replaced, but this is still a growing team and I want us to stay together."