Twitter user @ExWHUemployee is a well-respected source of news and gossip with close links at the club.
He first revealed the club's interest in both Joe Hart and Javier Hernandez, both of whom have now signed for the Hammers.
Speaking on The West Ham Way podcast, @ExWHUemployee discussed numerous possible deals that could be done this summer.
Those include Adrian leaving, a possible arrival of Victor Valdes and a return for Rob Green.
But it would be a swoop for Gray, 26, that would excite Hammers fans the most.
@ExWHUemployee said: "Andre Gray is still a potential one. He's out of contract in a year and if we can sell Fletcher, and if we maybe sell Feghouli as well, that opens up the possibility for him.
"I do know the board and Bilic were keen on him being a second-choice striker.
"If Adrian goes, we're going to need a back-up keeper. There's a number that we've looked at.
"Ideally the club want to sign some young players to bring through, build up and develop.
"You're looking at Daniel Bentley, there's a guy who plays for Sheffield United, Simon Moore.
"If we can't bring these players in because they cost money, there's a couple more players who will be available on a loan or free transfer.
"Valdes, who was at Middlesbrough, is available on a free. Whether he'll come as a back-up keeper, I don't know. I think we'd look at him.
"There's potential for Rob Green to come back, believe it or not. There's a guy at Newcastle called Karl Darlow as well who falls more into the young prospect category.
"It's going to depend on how willing these clubs are to sell.
"If we do sell Adrian, that'll push us into signing these players and it'll be more likely to be someone out of contract because you can get them quickly."
The Hammers have also shown an interest in Lazio forward Keita Balde but the deal now appears to be off.
Interest in Celtic's Moussa Dembele and Benfica frontman Raul Jimenez is also likely to amount to nothing.
@ExWHUemployee added: "The guy at Lazio, Keita Balde. We did submit a bid for him but his interest wasn't really there on his part. He didn't particularly want to come to us.
"I think it was more the fact we'd sign him or Arnautovic and obviously Arnautovic has already signed now so I don't think that signing is likely to happen.
"I think Moussa Dembele is going to be out of our price range. We have scouted him before. I don't think we're going to get him this window.
"Jimenez is attracting interest from a number of clubs. I don't think we'll go for him because of his value but if he can come in on loan the value can decrease, that might be an option."
