The 24-year-old is the latest name to be linked with a move to the Premier League, having previously attracted interest from Arsene Wenger during his time as Arsenal boss.
Almiron is highly-valued by Atlanta and is one of the brightest prospects in MLS at present.
On Thursday afternoon, the Guardian reported both Newcastle and West Ham were chasing the player.
However, Express Sport understands Atlanta have no intention of selling Almiron during the summer transfer window.
The US outfit currently sit top of the Eastern Conference and are among the favourites to lift the MLS Cup in December.
The transfer window across the pond closes next month and will not reopen until February, meaning European outfits will be forced to wait until 2019 to land Almiron.
The Paraguay international has been chased by some big European clubs in previous transfer windows, with Arsenal and Inter Milan expressing an interest last year.
Speaking back in April, Atlanta United chief Darren Eales said: â€śThere are rumours galore about all of our players.
â€śThatâ€™s the nature of soccer. We are focused on doing as well as we can this season.
â€śIt certainly wonâ€™t happen in the foreseeable future.â€ť
Newcastle and West Ham fans have witnessed entirely different transfer windows so far this summer.
Rafa Benitez continues to try and secure deals for the north east outfit, but has only managed to sign Martin Dubravka and Kenedy, who were both on loan at the club last term, and free agent Ki Sung-yueng.
The Hammers, however, have spent big under the guidance of new boss Manuel Pellegrini.
The Chilean has so far brought in Jack Wilshere, Felipe Anderson, Andriy Yarmolenko, Ryan Fredericks, Lukasz Fabianski, Issa Diop and Fabian Balbuena.