A joint statement from the charities said the merger would help "improve the life chances of children and strengthen the quality of family life in the UK".
A spokeswoman for the Family and Parenting Institute said that, although discussions were at an advanced stage, it was not possible to give details of possible changes to staff numbers.
Neither organisation was able to confirm when the merger was expected to be completed or how long talks had been going on.
According to figures from the Charity Commission website, the Family and Parenting Institute employs 33 staff and had an income of almost £8.6m in 2010/11; the Daycare Trust employs 17 staff and had an income of £1.2m in 2010/11.
Christine Farnish, chair of the Family and Parenting Institute, said she looked forward to forming a new organisation with the Daycare Trust.
"I am delighted that the Family and Parenting Institute and the Daycare Trust have committed to combine their respective strengths into a single charity, able to speak out powerfully on behalf of parents and families and promote the childcare agenda.
Maggie Darling, chair of the Daycare Trust, said: "This is an exciting opportunity to bring together the major strengths of both charities.
"In challenging times it is vital that we move forward together to make the UK a family-friendly country where the social and economic benefits of high-quality and affordable childcare continue to be valued.
"I believe joining forces is the best way forward to serve our beneficiaries in the years to come."