GKN explained that the board had unanimously rejected the proposal, having concluded that it "is entirely opportunistic and that the terms fundamentally undervalue the Company and its prospects". Melrose's share price has also advanced and is 6.56 percent better off at 229.10p.
Under the stock market rules, Melrose is now required to either announce a firm offer by 5pm on 9 February, or announce that it is no longer interested.
It said both businesses would benefit from being separate companies with distinct investment profiles and capital allocation policies.
Last year, lower profit margins and cash generation prompted GKN to conduct a wide-ranging review of its business.
The firm issued a profit warning in October over problems at its aerospace division.
A two-year programme dubbed "Project Boost" has been launched to "significantly" improve performance across the business.
Also included in the statement issued today reveals plans to split the aerospace and automotive divisions into separate companies, and that Anne Stevens, now Interim Chief Executive, agreeing to become the Group's new Chief Executive with immediate effect.
The BBC quoted Nicholas Hyett, an analyst at Hargreaves Lansdown, as commenting that the split had been "on the cards for years" because there was little crossover between the two businesses.
'Historically, the pension deficit has held the group together, but with the sprawling footprint likely to have contributed to recent profit warnings, the reasons for divorce now seem to outweigh the costs of splitting'.
GKN also announced that Anne Stevens, now its interim chief executive, has agreed to take over as the group's new chief executive with immediate effect.
The decision followed a £130m writedown in GKN's aerospace division, which Mr Cummings had been running. This is before accounting for the previously announced substantial write-offs in the North American Aerospace business.
Ms Stevens, who at 69 has extensive experience in the aerospace and automotive sectors, said she would instill a much stronger performance and accountability culture at the group, which employs 58,000 people across 30 countries.
The company's origins can be traced back to the Dowlais Iron Co, near Merthyr Tydfil in South Wales, in 1759.
Melrose Industries specialises in taking over troubled or underperforming industrial groups.
Speculation has been ongoing for a while as to whether the firm would be a takeover target or decide to break itself up.
Last August the firm acquired United States company Nortek for £2,2bn.