Garner is on-loan with Forest from Manchester United to the end of this term.
Former United defender Blackett would love to see Garner stay at the club next season.
“Hopefully. I'm not sure what his plans are in his own mind or what the manager has planned for him," he told NottinghamshireLive.
“But we want the best players here. Jimmy is one of our best players now, and he's showing that.
“If he continues, hopefully he'll still be here."