The Irish-based consortium have said they notified the club by letter last week that they have an agreement in principle to assume a 37 per cent shareholding in the Championship club.
This is said to be made up of former chairman John Ryan's 23 per cent and another 14 per cent from minor shareholders.
Sequentia set Doncaster a deadline of two days ago to respond to the letter, but have yet to receive an answer.
Current director Terry Bramall, whose 23 per cent stake Sequentia sought to gain, said at the end of November that Rovers had rejected Sequentia's takeover bid after months of negotiations that eventually ended in Ryan's resignation.
But the investment fund company have come back again and believe Bramall and fellow shareholder Dick Watson - who also owns 23 per cent - should act now.
Sequentia say they have a £20m kitty to spend on Rovers, with £10m earmarked for the takeover of the club and the same amount to be given to manager Paul Dickov to strengthen a squad that is battling to keep its head above water in the second tier.
With that in mind, Sequentia are keen to move swiftly, given that the opening of the January transfer window is less than two weeks away.
"We would like to gain control as soon as possible so that we can put investment into the club to help Doncaster avoid relegation," said Sequentia spokesman Kevin Phelan.
"The ball is in the court of Mr Watson and Mr Bramall.
"But it needs to be done sooner rather than later because at the end of January time starts to run away to the end of the season very quickly.
"If they are not going to put the money in themselves we are here, prepared to put the money in. We have proven we have £20m."
Sequentia's agreed stakehold would make them the single largest shareholder in the club, but they say they do not want to act until they can acquire every share.
The remaining 17 per cent not controlled by Bramall, Watson or, in principle, themselves, is shared between minority shareholders.
"We want to acquire all the shares simultaneously," continued Phelan.
"Those 37 per cent of shares are ready to be transferred to us at an agreed price as and when we acquire the rest of the club.
"Those shareholders have all signed up to it.
"Theoretically, if we wanted to take that 37 per cent shareholding now, we could.
"But we are trying to do this in a friendly manner."
The Sequentia interest has hung over the club since the start of the season.
It has already proven divisive in the club's corridors of power with Ryan resigning over his fellow directors' refusal to accept the Sequentia offer.