Current owners Tom Hicks and George Gillett had been looking for about 600 million pounds, according to local media, and Broughton said the pair had broken written agreements in a boardroom battle that is complicating the sale.
The American duo instructed Barclays Capital in April to find a buyer and appointed British Airways chairman Broughton to oversee the sale.
"Part of the terms of me taking on the role was that they gave a written undertaking that only I could change the board... and they also gave a written undertaking that they would not interfere and frustrate any reasonable sale," Broughton told Sky Sports News.
"This is frankly a flagrant abuse of those two written undertakings.
"It was the last chance for them to leave Liverpool with their heads high. It's a pity they've chosen to go this route."
On Tuesday, Hicks and Gillett sought to remove managing director Christian Purslow and commercial director Ian Ayre from the board, trying to replace them with Mack Hicks and Lori Kay McCutcheon, in a bid to keep control of the club.
Broughton said the 300 million pounds price tag included 200 million in writing down all acquisition debt and taking on some additional working capital debts and other liabilities.
The five-times European champions owe 237 million pounds, mainly to creditors Royal Bank of Scotland who have set a deadline of October 15 for the debt to be refinanced.
Broughton said by selling to NESV, Liverpool should be able to emulate the Boston Red Sox Major League Baseball team, also owned by NESV, in turning around their fortunes on the field.
He said there would be money for new players and to create a 60,000-seater stadium in a "short timetable" - whether it be a new ground or an expansion of Anfield.
"They (NESV) want to be judged by what they do rather than by what they say and can demonstrate what they plan to do by what they have done," said Broughton.
"(The Red Sox was) a classic example of taking a very famous, traditionally historic major team which has seen better days and restoring them to their glory. I think it is a parallel which demonstrates action.
"Their mentality is all about winning. They have invested a lot of money in players there, they have committed to making the necessary investment in players at Liverpool."
NESV is headed by John W Henry and Tom Werner. In 2004, two years after they took over the Red Sox, the team won their first World Series since 1918. They secured the title again in 2007.
Hicks and Gillett bought Liverpool in February 2007 for 218.9 million pounds and have been unpopular with fans for burdening the club with debt, leaving little in the transfer pot to buy new players and strengthen the squad.
Liverpool, English champions 18 times, have made their worst start to a season in more than half a century.
