The process is being run through the Crown Commercial Service. The successful agency will be appointed on a three-year contract.
The benefit, which was unveiled in 2013, provides a basic allowance and extra support for children, disability, housing and caring.
Universal Credit is set to replace Working Tax Credit, Child Tax Credit, Housing Benefit, Income Support, income-based Jobseeker’s Allowance and income-related Employment and Support Allowance.
The DWP is led by the work and pensions secretary, Iain Duncan-Smith. In January last year, it appointed Engine to handle activity around workplace pensions after a pitch.
The DWP did not respond to requests for comment.