Celtic have turned down two offers for the English striker from Norwich City this month.
The 24-year-old's two goals in the 4-0 win over Dundee United last night takes his tally for the season to 22.
And it has emerged the hit man, who is also attracting interest from Spurs, has rejected a contract offer from the Hoops.
Mulgrew, though, is keen to see his team- mate remain in Glasgow with two games against Italian giants Juve to play in February and March.
And he believes any interested parties will need to bid far higher than the £5million that the Canaries had rejected this week.
He said: "Gary is a big player for us. You have seen how good he is for us these last few days.
"We want to keep every-body together. There is a good squad here and we all get on well. We have a good team spirit.
"We don't want to lose anybody. Hoops is a good lad. He doesn't let it get to his head. He just gets on with his job.
"You saw that against Dundee United last night and Hearts on Saturday.
"He has been a good player for us all season, even before all the specu-lation about his future.
"We see Hoops day in, day out. We know his quality, we know what he can do, we see the goals he scores. I think he is worth a lot more.
"You can see his touch, his awareness and his goalscoring ability whenever he plays. He is a top player."
Mulgrew wants Celtic to remain focused on domestic football and not let their minds wander to the Juventus clashes.
He said: "We have to concentrate on getting the domestic stuff right. We will deal with Juventus when it comes."