A council dispute is threatening to force Forest to leave their stadium.
After defeat to Chelsea, Dawson told BBC Sport: "It's a special place, the City Ground, right on the Trent.
"I don't want them to move. I was a young eight-year-old watching that team and fortunately I got to play for them for a long time. It's iconic, it's a great place to play and watch your football.
"Those fans are amazing and last year they kept them up. Unfortunately it's not quite the scenes we saw last season when they beat Arsenal."