Saturday's hard-fought fourth-round victory over Aldershot handed the Teessiders a fifth-round clash with either European champions Chelsea or League One side Brentford at the Riverside Stadium and their manager can hardly wait.
Mowbray said: "I grew up watching Boro at Ayresome Park and I remember some amazing FA Cup fifth-round ties.
"I think the FA Cup starts getting exciting at the fifth round stage. You are one win away from the quarter-finals.
"Cup football is exciting because it's something different. You are away from 46 games of hard slog.
"Whatever happens, as I hoped, we won't be playing another Championship team and we are also at home, so you can't ask for any more than that."