Carroll, a free agent after leaving Greek champions Olympiacos, played in the Magpies' 1-0 defeat at Halifax on Saturday.
Derry plans to hold talks with the 36-year-old Northern Ireland international this week about a deal to bring him to Meadow Lane.
"I will have a sit down with him and have a chat. It would be nice if we can sort something out," Derry told reporters following the defeat at Halifax.
"He is the type of keeper I am looking for. He's a man. I heard him talking to the back four and he's got a great mentality.
"He didn't have much chance with the goal, but he commanded his box well and that's what you get with a goalkeeper of his experience."
Notts are in the market for a goalkeeper with experience after losing Bartosz Bialkowski to Ipswich earlier this month.
Breaking news, transfer gossip, line ups and goal alerts from your football club - delivered direct to your mobile. Sign up for Sky Sports Alerts