Fuming Celtic chiefs have kicked out two Canaries bids - the second of them around £5.5million.
Mulgrew told the Scottish Sun: "Are Norwich's offers a bit derisory? Of course. We see Hoops day in, day out. We know his quality and what he can do.
"Everyone sees the goals he scores. So, yeah, I think he is worth a lot more than that. He's a big player. We want to keep everybody together because there is a good squad here.
"We have good players and we all get on well, so we don't want to lose anybody."