Almiron joined the Magpies from MLS side Atlanta United for around £20m in 2019 and has since chipped in with 30 goals and 12 assists in 209 appearances across all competitions.
The 30-year-old still has two years left on his contract at St James' Park, but he has regularly been linked with a possible summer exit amid interest from clubs abroad.
An unnamed team from the Saudi Pro League are understood to have held talks with Newcastle over a deal for Almiron, but a potential switch to the Middle East has failed to materialise for the winger thus far.
A return to the USA has now been mooted for Almiron, with Chronicle Live reporting that the Magpies have rejected an opening offer for the Paraguay international from Charlotte FC, who are managed by ex-Aston Villa and Norwich City boss Dean Smith.
The report adds that Newcastle have informed Almiron that he remains an important part of Eddie Howe's first-team plans and the Magpies do not intend to sell the winger on the cheap.
Crystal Palace 'reject' £20m Andersen offer from Fulham
Staying in the Premier League and Fulham have reportedly failed with an offer to sign Joachim Andersen from Crystal Palace.
The 28-year-old centre-back spent the 2020-21 campaign on loan with the Cottagers, making 31 appearances, before completing a permanent move to Palace form Lyon the following summer.
Andersen has since established himself as an important first-team player for the Eagles, making 112 appearances in all competitions including 38 Premier League outings last season.
Football Insider reports that Fulham have tabled a £20m bid to re-sign Andersen this summer, but Palace have swiftly rejected the offer.
The report adds that Fulham's opening bid is 'nowhere near' Palace's valuation of the Denmark international, who cost £17m three seasons ago and has two years remaining on his contract at Selhurst Park.
It is understood that Palace are 'very unlikely' to sell centre-back duo Andersen and Marc Guehi, with the latter currently the subject of strong interest from Newcastle.
Girona 'agree' £6.8m deal for Aberdeen striker
Elsewhere, La Liga outfit Girona are reportedly closing in on the signing of Aberdeen striker Bojan Miovski.
The 25-year-old was brought to tears as he was given a heroes send-off from the Aberdeen supporters following their 3-1 home win over St Mirren in the Scottish Premiership last weekend.
Miovski has been as an integral first-team player for the Dons since joining in 2022, scoring 44 goals in 97 games across all tournaments, but a move to Spain is edging closer for the striker.
According to Sky Sports News, Aberdeen are set to land a club-record transfer fee of around £6.8m with the sale of Miovski to Girona, surpassing the £6.5m they received from Liverpool for Calvin Ramsey in 2022.
It is understood that the two clubs are close to finalising the necessary paperwork and personal terms are not expected to be an issue.
Miovski, a 22-cap North Macedonia international, is believed to be keen to join Girona who will compete in the newly-expanded 2024-25 Champions League after finishing third in La Liga last season.