Almiron starred as Atlanta won the MLS Cup last week in just its second season, the Paraguay international having been a key figure since signing as a Designated Player ahead of the club's debut year.
His fine form in MLS has led to links to several European clubs, most notably Newcastle United, with the speculation ramping up ahead of the January transfer window.
However, despite reports that Almiron was closing in on a move to England, Atlanta insists it is yet to agree a deal.
Asked if the club had received an acceptable offer, president Eales replied: "No, absolutely not."
River Plate's Copa Libertadores hero Gonzalo Martinez has spoken of a potential move to Atlanta, and could take Almiron's place, but Eales is still waiting for an offer that suits all parties.
"We've got our three Designated Players, who have all been superb players, and they're all under long-term contracts," he said. "The reality is no different from anywhere around the world: if they're under contract and the right offer came at the right price, then it's something we'd consider.
"But you've got to bear in mind that we play in front of crowds of over 70,000 people and we've got a billionaire owner [Arthur Blank] who is ultra-competitive, who has seen an MLS Cup victory and wants to make sure that we go back there next year. It's going to need a serious offer for us to consider it.
"[Replacing departing stars] is something that we'll be working for if the right offer comes for any of the players on our team.
"It doesn't matter who they are, we're always working in the background to try to make sure we've got somebody to come in and make sure that we're a top team, competing for trophies year after year."
Explaining what would constitute "the right offer", Eales said: "From our perspective, there are three aspects.
"For the players, we want the players to succeed wherever that is if they leave Atlanta. It's good for the club, it's good for the league and for the player as well. That's obviously a factor.
"For the league, it's important, a league where we are all pioneers in trying to grow the game in America. It's important that it's a significant number for the league.
"For the club, it's also got to be the right figure for us. An aspect of that is that we want the player to go to a club where they can succeed, because that's good for everybody."
Eales is not surprised that Almiron's name is being discussed, comparing the Atlanta man's running style to that of Real Madrid superstar Gareth Bale.
"I've got total understanding of why clubs in Europe, in the Premier League are linking themselves to Miguel Almiron," Eales said. "He's a fantastic player and his speed with the ball is incredible. He's actually quicker with the ball than without it. In that sense, he reminds me a lot of Gareth Bale from when I was at Spurs.
"It's that ability where, once he's got the ball, he almost seems to go up a gear, which is quite unique.
"Miggy was one of the best players in both of our last All-Star games, against Real Madrid and Juventus. I can understand why there's a lot of speculation. He's a top talent who could play for top clubs around Europe."