Almiron has returned to pre-season training after being given an extended break following his involvement in Paraguay's Copa America campaign.
However, it is currently unclear whether Almiron will still be a Newcastle player when the transfer window closes next month.
According to Football Insider, the Paraguay international is in advanced talks to join an unnamed Saudi Arabian club.
The 30-year-old has been offered a lucrative deal and all parties are seemingly confident that a deal will be agreed.
Newcastle are willing to offload Almiron so they can bring in a new winger, with the Magpies believed to be pursuing a move for Chelsea's Noni Madueke.
Almiron, who joined Newcastle from Atalanta United in 2019, has scored 30 goals and provided 12 assists in 209 competitive appearances during his time with Magpies.
De Gea open to Genoa move
Meanwhile, former Manchester United goalkeeper David de Gea is reportedly interested in joining Serie A side Genoa.
De Gea is looking to revive his career after his 12-year association with Manchester United came to an end last summer.
The former Atletico Madrid goalkeeper has been linked with the Saudi Pro League and MLS, but it appears there is a chance he could complete a move to Italy.
According to Gianluca Di Marzio, Genoa are considering whether to sign De Gea, with the Spaniard open to the idea of joining the Serie A club.
Having competed in La Liga and the Premier League, De Gea is seemingly ready to try his luck in another major European league.
The report claims that Genoa must decide whether to sign the 33-year-old or turn their focus to other goalkeeper targets.
The Serie A side are in need of a new shot-stopper after seeing Josep Martinez complete a move to Inter Milan earlier this month.
Bologna confirm Hummels offer
Staying in Italy, Bologna CEO Claudio Fenucci has confirmed the club have presented a contract offer to experienced defender Mats Hummels.
The 35-year-old is searching for a new club after leaving Borussia Dortmund upon the expiry of his contract earlier this summer.
According to journalist Fabrizio Romano, Bologna had scheduled a medical for Hummels, but he has taken more time to decide his next move.
Bologna's chief executive has confirmed that the Italian club have made an offer and are waiting to receive his final response.
Fenucci told reporters: "Why does Hummels take some time? It's very normal, we spoke to him recently. It is right that he thinks about it, to arrive with the right motivations.
"We don't have to talk here about our conversations with Hummels, but we explained the project and the city to him. Many players have finished their careers here, the city has this attraction, it seems. There is no deadline, but if there are no conditions we have to look at other players as well."
Bologna are hoping to sign Hummels as a replacement for Riccardo Calafiori, who is set to complete a move to Arsenal.