Billy Davies' return to the managerial hot-seat at the City Ground has sparked Forest into life, with the Reds having won five in a row to climb back into the Championship play-off places.
Forest are now just nine points adrift of the top two with nine games remaining.
Collins feels anything is possible from this point, with Forest having established the kind of momentum which will have the rest of the division running scared.
He said: "Why not aim for automatic? Why can't we set our sights even higher, after everything that has happened so far under the new manager?
"We don't fear anyone. All the teams above us must be looking over their shoulders."
Davies is, however, keen to avoid being caught up in the promotion buzz, with Forest's run-in due to pitch them into direct competition with a number of fellow high-fliers.
He said after a 3-1 victory over Wolves on Saturday: "We are suddenly within nine points of being second in the table.
"I'm not looking at it like that. Honestly, it's just one game at a time. Staying in the top six will be tough enough, never mind anything else."