The two charities, which both provide support to unemployed people trying to get into work, announced in February that they had commissioned a feasibility study into a potential merger.
The study, carried out by the audit firm KPMG and concluded in May, found that a merger would be a positive move for both charities.
Roy O’Shaughnessy, chief executive of the CDG, said: "The independent feasibility study has told us that there is compelling evidence that blending our strengths and expertise is likely to be the best option, rather than remaining separate or working in a more informal partnership. However, until final decisions are made after due diligence, it’s very much business as usual for both the Shaw Trust and the CDG."
The two organisations are carrying out due diligence processes to assess the viability of a merger and how it might affect both organisations.
The Shaw Trust had an income of £112.6m in 2010/11 and CDG’s was £30.8m during the same year, according to figures on the Charity Commission’s website.
CDG is a prime contractor on the Work Programme, the Department for Work and Pensions’ main employment initiative.
It has a payment-by-results contract for east London worth up to £120m over five years and a 30 per cent share of two prime contracts with a private company, Maximus Employment & Training UK, which are worth up to about £35m each for the charity.
The Shaw Trust employs about 1,000 staff and CDG has about 300 employees.
Chris Melvin, interim chief executive of the Shaw Trust, said: "We know we both share similar values, but the study shows that together we could benefit from having a greater voice and increased capacity to respond to the needs of our service users.
"We could be a strong third sector force at a time of national economic and employment crisis, and at a time when delivery and innovation has never been needed more."