Officers were called on Monday night to Hall Gate, which is known for its nightlife scene.
A South Yorkshire Police spokesman said: “We were called at about 9.40pm on Monday to inform us of a reported disturbance at a premises on Hall Gate which continued out onto the street.
“A man is reported to have made threats towards members of the public in the street, before walking towards the Lord Nelson Pub, getting into a car and driving away.
“Officers are conducting enquiries to determine what happened, and are checking CCTV in the area.
Anyone in the area at the time or has CCTV footage should call 101, quoting incident number 980 of 14 March.
Alternatively, you can stay completely anonymous by contacting independent charity Crimestoppers via Crimestoppers-uk.org or by calling their UK Contact Centre on 0800 555 111.