The male was arrested after he self-presented at Merseyside Police HQ just after 2.30am on Friday.
Officers then attended at an address in Prince Alfred Road, Wavertree, where they found the body of a 20-year-old woman.
The arrested male, who comes from Wavertree, will be interviewed by detectives today and a Home Office post mortem will be carried out to establish the cause of death. Officers are not looking for anyone else in connection with the incident and house-to-house inquiries are ongoing.
The victim’s next of kin have been informed and specialist officers are supporting the family of the victim at this difficult time.
Detective Chief Inspector Paul Speight said: “An investigation is now underway following this tragic incident and I am keen to speak to anyone with information which may be able to assist our enquiries.
“If you were in the area at the time, saw or heard any suspicious behaviour, or have any CCTV or dashcam footage, please come forward. Any information, no matter how small, could prove vital to our investigation.”
If you have any information, or live locally and saw or heard anything, please contact @MerPolCC, 101 or Crimestoppers anonymously on 0800 555 111, quoting reference 0070 of 29 January.