The top flight offered a £50m support package for League One and Two clubs on Wednesday that was subsequently rejected by the EFL as they negotiate a better deal that includes the Championship.
This comes after the Premier League turned down 'Project Big Picture' that was formed by Liverpool and Manchester United and backed by EFL chairman Rick Parry.
Although Pomlett has not formally welcomed the rejected project or the top flight bailout, he does insist that something must be done and that Walsall must take advantage of the 'opportunity' before them.
"It doesn't really matter whether you call it 'Big Picture' or whatever name you put on it, the fact of the matter is this is an opportunity to readdress the balance in football," Pomlett said.
"The pyramid needs to be financed in a different way.
"As an EFL club, we are absolutely adamant that this is an opportunity to readdress the balance, to re-distribute the wealth in football, which is a very wealthy sport, and we won't get this opportunity again.
"We've stuck in pretty hard. This obviously caused some tough negotiations between the EFL and the Premier League and I suspect they'll continue for a while longer before we have a full resolution.
"The fact they're happening at all is good news and we watch those developments with interest and influence them. We've been on many calls this week with the EFL to try and influence that debate.
"It also relates to the fact, of course, to the fans coming back to the stadium. We're all missing you terribly.
"We're putting the government under increasing the pressure, I say we, the whole of the EFL and 200,000 fans now that have signed a petition to allow fans back into our stadiums in a socially distanced way.
"We will continue to exert pressure on the government until that decision is made. The pressure is mounting on them to allow it."