The offer from Melrose, valuing the business at 405 pence ($5.48) per share, sent shares in GKN up 20 per cent to 398p this morning.
The company has a major operation in Telford and employs about 340 people at Hadley Park making structural parts including wheels.
Employing 58,000 people across 30 countries in aerospace and automotive engineering, 258-year-old GKN stunned the market in October when it cut its profit outlook due to problems in the aerospace division.
The downturn led to the dismissal of the Aerospace head, Kevin Cummings, who had been due to takeover as the future group chief executive in January.
GKN said today it had now appointed Anne Stevens to run the group on a permanent basis after she took up the role of interim CEO in November.
"The board of GKN has considered the proposal ... and has unanimously rejected it, having concluded that the proposal is entirely opportunistic and that the terms fundamentally undervalue the company and its prospects," it said.
Under the UK's takeover rules, Melrose now has until 5pm on February 9 to "put up or shut up" – either announce a firm bid or step away for the next six months, absent any change in circumstances.
GKN will now work on plans to split the business between its aerospace and automotive divisions.
It added that it was trading in line with expectations.
Commenting about the appointment of Ms Stevens, chairman Mike Turner said: "The board believes that Anne Stevens has the track record to transform GKN. After a successful turnaround of The Ford Motor Company's businesses in Mexico, Canada and South America, she was appointed as chief operating officer for the Americas where she developed the transformation plan for Ford's US business.
"Her operational and strategic skills are ideally suited to GKN and the board is very impressed with the contribution she has made so far in setting out plans for a significant improvement in the group's performance."