Since returning from a broken leg, the 26-year-old has surprised Liverpool fans with an enterprising series of displays that have led to a call-up to Sven-Goran Eriksson's England squad.
Carragher came tantalisingly close to claiming a goal in recent home games with Everton and Portsmouth, and Thompson is eager to see Carragher break his duck this season.
Thompson said: "I am delighted Jamie is back in for England, he can play five roles for them and us. To be back in the England squad five months after breaking a leg is a great credit to Jamie and his professionalism.
"But I now want to see him score. He has been encouraged to get forward more and people could see him popping up in the box having shots in the Cup tie at the weekend.
"Now I just want to see him get a goal for us. Then he can start saying he can be an overlapping winger as well."