A 30-year-old man was detained last night in the Bramley area of the city in connection with the incident, which happened on land off Redcote Lane in Kirkstall on Monday.
A 23-year-old woman was leaving Pure gym at about 5.50pm when she was grabbed and dragged into bushes but managed to fight off her attacker and flee.
Det Chief Insp Elizabeth Belton, from West Yorkshire Police’s homicide and major enquiry team, said today: “A 30-year-old local man was arrested last night from an address in the Bramley area.
“He remains in police custody after he was arrested on suspicion of attempted murder and attempted rape.”
Police are also investigating an assault on a 39-year-old woman that took place early yesterday while she was out jogging on the Leeds and Liverpool canal towpath between the A58 inner ring road and Viaduct Road in Kirkstall.