A spokeswoman for Asylum Aid said the charities believed they could provide a wider range of services by merging and thus help more refugees and migrants.
She said the merger was subject to due diligence and the final approval of both charities’ trustees and members.
If the merger were to go ahead, the new organisation would be a partnership of equals, with both names and brands initially retained, the spokeswoman said.
Once any merger took place, she said, a new board of trustees would be appointed. It would review branding and decide whether any changes were needed.
Trustees would also review whether the merged charity needed to keep both charities’ buildings and offices, the spokeswoman said.
It was unlikely that either charity would make any redundancies, although final decisions on staffing would be taken once the merger was ratified, she said.
She said Wayne Myslik, chief executive of Asylum Aid, would lead the new organisation and the boards of trustees and senior management teams would be merged.
Ros Lucas, chief executive of MRC, had previously announced her intention to retire, the spokeswoman said.
MRC, which employs 11 people, has an operating income of approximately £545,000 a year, compared with about £850,000 a year for Asylum Aid, which has 12 staff.
The spokeswoman said both charities were in strong financial positions and the merger was intended to enhance the services both charities offer.
Catherine Briddick, chair of Asylum Aid, said: "This proposed merger of two strong and like-minded organisations dedicated to serving the interests of migrants and refugees is an exciting step forward. We will bring together the wealth of experience and knowledge of both organisations in order to offer the very best support for migrants and refugees."
Helen Rice, chair of MRC, said: "A merger would provide us with the opportunity to support even more migrants and refugees with an even wider range of services, while helping to strengthen the organisation for the future. We are committed to keeping the people we support at the centre of everything we do and are confident that this partnership would mean we could deliver an even better service for them."
The two charities hope to reach a final decision on whether to merge by May, with any merger taking place over the summer, the Asylum Aid spokeswoman said.