The Bulgarian ended Murray's title defence at SW19 on Wednesday with a 6-1 7-6(4) 6-2 victory on Centre Court.
Despite some big names still left in the draw, Connors believes that Dimitrov could go all the way.
"Dimitrov is in a semi-final and he will say why can't he beat [Roger] Federer or [Novak] Djokovic and win the title," the American told BBC Sport.
"He played spectacular tennis today. It won't get easier so he has to lift his level again. I don't think he is just satisfied with being in the semi-final."
Dimitrov will face either Djokovic or Marin Cilic in the semi-finals.