Derby runs 18 children's centres, but says that there is a need to target resources at the most needy children and families.
The move means that 2,399 under-fives who currently use the six threatened centres will be forced to find other provision.
The council cites low take-up of children's centre services in some areas and says that underused facilities could be offered to schools and used to expand provision for autistic children.
Council papers state that the local authority will receive £1.8m less in funding in the new Early Intervention Grant - which includes children's centre funding - for 2011/12 and will lose a further £300,000 the following year.
The council plans to close four children's centres in the least disadvantaged areas - Mickleover/Littleover, South Chaddesden, Oakwood and Chellaston - and offer the buildings to the primary schools where they are based.
The two other centres, Derwent and Peartree, have no permanent sites and operate from community and school buildings. Plans include re-locating provision from Derwent, which the council said is only used by 14.6 per cent of under-fives in its target area. Services offered by Peartree would instead run out of Rosehill and Babington children's centres. Currently, take-up is just over 50 per cent.
Councillor Evonne Williams, cabinet member for children and young people, said, 'The savings we have to find mean we are having to make some tough calls. But the proposals for the youth and children's centres show how we can turn the situation into an opportunity to provide a more targeted and popular service where it is most needed. Our proposals would offer up much needed space for schools.'
An eight-week consultation on the plans starts next week.
