The suspects, a man aged 26 and a 19-year-old woman, are being held over a knife attack in Wilcox Road, Fox Hill, yesterday.
Emergency services were deployed at around 8am after a man in his 20s was found with stab wounds.
He was taken to hospital where his condition is thought to be stable.
South Yorkshire Police said: “Anyone with information which could assist with our enquiries, who was in the area yesterday morning and saw or heard anything suspicious, or who may have CCTV or dash cam footage which captured any of the incident, is asked to call 101, quoting incident number 166 of May 11.
“Alternatively, you can stay completely anonymous by contacting the independent charity Crimestoppers via their website Crimestoppers-uk.org or by calling their UK Contact Centre on 0800 555 111.”