The Weekend Australian has learned the Eels are keen to play Hindmarsh's final game at Homebush to help accommodate more fans.
The game will also act as the final matches for Eels winger Luke Burt and St George Illawarra hooker Dean Young.
"I'm trying to take a commercial position for the club and the good of the game and for Hindmarsh who has been a legend of the game," Parramatta chief executive Bob Bentley said.
"They're taking a hardline approach in that you've got an agreement, that's what the agreement is and if you don't play your game there we're going to hit you up for 100 grand.
"That will have a major impact on the decision we make when we give it full consideration because I'll be starting 100 grand behind from where I need to be if we do go to ANZ."
Parramatta Stadium director Luke Coleman downplayed the extent of the dispute.
"We're in discussions with the Parramatta NRL club but I wouldn't say we've got a battle on our hands," he said.
"It's all fairly civilised.
"It's very much up to the club where they're going to play their games.
"We don't even know what day it's on yet because we haven't heard from the NRL."
The Olympic venue holds 80,000 fans compared with the 21,000-seat capacity at Parramatta Stadium and officials are optimistic that up to 40,000 people could turn up to farewell three of the game's favourite sons - particularly Hindmarsh, who is the heart and soul of the Eels.
While the Eels have an agreement until the end of next year to play their matches against South Sydney and Canterbury at ANZ Stadium, they are still contracted to play a certain number of games at Parramatta Stadium each season.
Shifting the Dragons game would breach that deal.
As a result, Parramatta Stadium has informed the club it will not budge on its stance of a $100,000 exit fee.
The parties have been in talks for more than a month.
Time is running out with the NRL needing to know by the middle of next week where the match will be played so it can finalise its draw for round 26.
It is not known at this stage if the Nine Network will select the Eels-Dragons game as one of its free-to-air games.
Heading into this weekend the Dragons were still in line for the finals while the Eels have made a late-season rally following the departure of coach Stephen Kearney and are desperately trying to avoid the wooden spoon.
The dispute over Hindmarsh's last game could not come at a worse time for Parramatta Stadium as its five-year contract with the Eels is up at the end of the season.
While there is no suggestion the Eels will abandon the ground entirely as South Sydney did when it left the SFS to head to ANZ Stadium for a better deal, it could still affect the number of home games the club plays there from next season. "It's obviously an opportunity for us to leverage the best outcome we can," Bentley said.
"We need to be flexible to accommodate our fans and make sure we don't get locked into a position that we can't get out of or it costs us to get out of.
"I don't think we'd be in a position to take all our games to ANZ but it might open the door to take a few more or even play a few games somewhere else like regional NSW for our country fans."