According to media reports, the new deal includes an attempt to address fears that shareholders who wanted to leave would lose out.
The latest offer, according to the Financial Times, includes a cash alternative of 40p a share on top of 86p in cash, which was part of an original offer already rejected by ITV's board.
This would allow investors not wanting to be part of the newly restructured ITV to take their money and run.
The consortium, which involves Apax Partners, Blackstone and Goldman Sachs, is also be considering a merger with Five to further bolster the deal.
Last week, ITV rejected a £1.3bn bid by the consortium in exchange for 48% of the company.
Other plans, should the consortium be successful, include using services such as Top Up TV to re-enter ITV into the pay TV market, an avenue it has not exploited since the collapse of ITV Digital.
The consortium is also expected to bring in its own management team, including installing former BBC director general Dyke as chief executive in place of Charles Allen.
Dyke is understood to have a list of industry executives he wants to bring into ITV to turn it around. One of their plans includes the importing of more high-quality US drama such as 'Desperate Housewives', which ITV has traditionally shied away from.
According to the FT, it is not known whether the board will be swayed by the latest bid, although so far the largest shareholder Fidelity, has expressed an interest.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .