The 30-year-old former Manchester City and Chelsea defender has one year remaining on his contract but Birch warned his salary, and that of a number of the club's other high-earners, could see Pompey go into liquidation before the start of the new season.
Birch has imposed a salary cap, and an offer to buy the club by former owner Balu Chainrai is on condition that high earners like Ben Haim are off the wage bill.
The Israel international spoke to Sky Sports News after Birch told The Independent that the player and his agent Pini Zahavi were "not helping" the situation at Fratton Park.
Ben Haim said: "I've lost a lot of money, but it's not about the figures. It's over £2.5m net but I'm prepared to lose more, I'm prepared to help the club and lose more money.
"On the other hand, the administrator's fee is not less than what I earn. Nobody talks about that, so I prefer to lose more but he has to cut his fees as well.
"I can say when it went to administration we sat with the administrator, and in five to 10 minutes we had a deal.
"We agreed everything, Trevor spoke with us but then he disappeared for two months, so it's not our fault.
"He forgot that you have to negotiate with the players and not with the press. The press are not going to sign a compromise, they have to sit with us and tell us the figures exactly."
A Portsmouth fans' group had earlier made a last-ditch plea to Pompey's senior players to take a pay cut. It is understood eight senior players have yet to reach agreement with the club over unpaid salaries.
Supporters' group SOS Pompey handed over an open letter to the players at Portsmouth's Eastleigh training ground on Monday morning in an attempt to make them compromise on their wages.
SOS spokesman Bob Beech told BBC Solent: "This is the end game for Pompey, in a couple of weeks it will be over.
"Some players were excellent and stopped to listen to what we said, others as expected weren't interested and drove straight on.
"At the end of the day, they have contracts and they expect those contracts to be paid and that is not an unreasonable stance to take.
"But the well is dry and if they stay and keep their demands going then there will be no club and they will end up with nothing."
In the letter, the fans said they sympathised with the players due to the money they had lost, but urged them to "demonstrate that footballers aren't the shallow, selfish people portrayed in the press".
The letter said: "With everything that has happened you, like us supporters, have every right to be angry, you are as much a victim of the incompetence that has left our club teetering on the brink as anyone.
"Now though, you have the chance to write your name in the history of our club, the decisions that you make will decide whether 114 years of history come to an end."