The Leeds Crisis Centre, which provides free, short-term counselling and support for adults, is likely to be closed with council chiefs making a decision next week.
The centre has 17 staff and costs the council 696,000 a year to run. A Leeds City Council spokeswoman said counselling services were not a statutory function of local authorities, and there was no evidence that any other councils in the country provided them.
There were 1,435 referrals last year but only 504 people actually received a counselling service. Existing users will complete their counselling. The council is in discussion with NHS mental health services to see what redeployment opportunities may be available for staff.