Philip Beard, who is heading up PAI Capital, joined White and Jordan on Tuesday to discuss the efforts to purchase the Premier League club.
Current owners David Gold and David Sullivan insist the club is not for sale and claimed that no proof of funds were provided after a first bid was said to be made.
Beard, who is the former chief executive of QPR, told talkSPORT: "I've got the utmost respect for Mr Gold, Mr Sullivan and Mrs Brady - we are interested and we are interested for one or two reasons.
"We think we could do something with West Ham. We think if the price is right they will sell, so we put together a bid. We put together proof of funds and for some reason West Ham said they haven't had a formal bid and hadn't had proof of funds.
"I think it's only right for West Ham fans to know that we have made a bid.
"The challenge seems to be that Mr Sullivan seems to have a much higher value.
"Whatever you spend on a business, especially in football, the more you spend the less you can invest in the team and squad.
"There's a realistic value we think that should be acceptable and pretty much thought was accepted, but now the goalposts have changed."
When asked if a second bid will go in, Beard said: "That's the plan. I'm not going to give any numbers out about what it is going to go in as, but as Simon has said, it is clear that Mr Sullivan, Mr Gold and Mrs Brady own the club, particularly Mr Sullivan and Mr Gold.
"It is their right to turn down any offer.
"I want to be able to be a better communicator, that will only happen with this project if we buy the club.
"One of the things that really is important to me is that the fans are everything to a football club."
Beard also said the Olympic Stadium is being under-utilised and wanted to improve fan experience, as well as investing in the team.
Former Crystal Palace owner Jordan, though, questioned the way Beard and the consortium is going about trying to buy the club and scrutinised their motives.
He said: "Philip, there's an element of irony coming onto a radio show and talking about transparency about how a transaction will manufacture itself without being transparent.
"If you want to buy a football club, having bought and sold football clubs and bought and sold businesses, the way you appear to be going about it is the anthesis of how I would buy a football club.
"Sitting on talkSPORT is not the way you buy a football club, buying football clubs is finding some sort of accord with the owners and using professional people to do it.
"My understanding is you've put a proof of funds in as a letter saying you've got the funds without a great deal of qualification behind that.
"You can't sit here and say 'I want to set the record straight and put people into the picture' - there is an element of playing to the gallery.
"Everybody knows that West Ham fans have been nothing but upset about the move from the Boleyn to the Olympic Stadium.
"You suggesting you are going to make it a better experience and better stadium is you playing to the gallery.
"I would have suspected there is an element of naivety about people you've bought into your consortium with Rio Ferdinand and Anton Ferdinand.
"Rio Ferdinand has been advocating all summer that Declan Rice be sold to Manchester United, so there's a little bit of naivety in bringing him into the mix.
"The notion of trying to buy a football club and dragging the current owners into the public domain over an unsightly sentiment of who has made an offer and how much that was for, whether that offer was put in place.
"I've had a conversation with a couple of them, it's fair to say I'm no cheerleader for David Gold and David Sullivan. I know perfectly well what they are capable of, but it's their business.
"If you knock on the door and say 'I want to buy your business or your house for X,Y,Z and they say no and want more than that, you can't sit in the public domain crying foul because they want more money for the business.
"Proof of funds isn't difficult, I've bought a football club and I went in and wrote a cheque out.
"The reality of it is that you are saying this model only works, and it is a property play because you are going to enable the development of the footprint around it to be giving you revenue streams to repay you money in the first place and service the demands of the football club going forward."
Gold and Sullivan bought West Ham in 2010 and have endured a fractured relationship with fans at times.
They moved the club away from Upton Park and into the London Stadium, the former London 2020 Olympic Stadium that was build for athletics events, and have often been a source of frustration for supporters.
The pair have always insisted the club is not for sale, though, telling talkSPORT's Jim White that last summer when calls for their departure grew loudest.
Despite early fears, West Ham had a brilliant season finishing 6th in the Premier League and will be playing in the Europa League this season.
David Moyes signed a contract extension and the pressure will be on to repeat that feat in 2021/22.
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