The charity met Lord Hunt, the minister for medical research, last week to discuss its campaign.
After that meeting, the government-funded Medical Research Council agreed to meet the charity to discuss ways of helping it reach its fundraising target.
Although the council stressed it had not yet agreed to provide funding, the MNDA hailed its decision to discuss the issue as "a major breakthrough".
In November the charity told the Prime Minister it would find £7.5m from major donors if the Government agreed to pledge the same amount.
MNDA president and Liberal Democrat MP Lembit Opik, whose father died from the disease, said he was optimistic that the funding would be secured now that a meeting with the Medical Research Council was in the pipeline.
The council spends about £480m each year on medical research.