The 21-year-old became a fan favourite at Goodison Park last season after registering four goals and two assists in 35 Premier League games to help Everton secure survival.
Gordon was strongly linked with a move to Tottenham Hotspur at one stage, but the Lilywhites settled on a £60m deal for Richarlison instead.
According to Sky Sports News, Newcastle have now touched base with Everton to register their interest in Gordon, but the Magpies have not made an official offer for his signature.
However, Everton are determined to fend off interest for the England Under-21 international, whose deal at Goodison Park still has another three years left to run.
Meanwhile, the future of Italian attacker Federico Bernardeschi remains up in the air following his departure from Juventus as a free agent, but MLS could now be his next destination.
The 28-year-old spent five years at the Old Lady since a £36m move from Fiorentina and made 183 appearances in that time, although he only racked up 12 goals for the club.
One Italy international in Lorenzo Insigne has already signed for Toronto, and according to journalist Michael Singh, Bernardeschi could soon join his compatriot.
Singh reports that Bernardeschi would also be interested in a move to the MLS side, and talks between the two parties have now reached an advanced stage.
The attacker collected three Serie A titles, two Coppa Italias and two Supercoppa Italiana crowns with Juventus and amassed two goals and six assists from 36 games in all tournaments last term.
Another player who could be set to wave goodbye to one of Serie A's top clubs is Milan Skriniar, whose contract with Inter Milan now only has 12 months left before it expires.
The 27-year-old has been strongly linked with moves to both Chelsea and Paris Saint-Germain, and the duo have now been handed a major boost in their efforts to sign the centre-back.
Manager Simone Inzaghi has now admitted that Skriniar could leave in the current window, telling reporters: "Today [Skriniar] is an Inter player, last year he had an extraordinary season.
"On the 10th he will arrive for pre-season and then we will see what happens. Last year this week we talked to Romelu and fifteen days later he was gone. We all know that things can change very quickly during the transfer market."
Skriniar was an integral part of Inter's 2020-21 title-winning squad, and the Nerazzurri are reportedly after a fee of €80m (£68.4m) to sanction a sale.
Finally, West Ham United will seemingly be forced to abandon their alleged pursuit of Villarreal's Arnaut Danjuma, who dazzled and delighted for the Yellow Submarine last season.
The former Bournemouth man hit 16 goals and set up four more in 34 appearances last season, including six Champions League goals as Unai Emery's side reached the semi-finals.
Danjuma has been strongly linked with a return to the Premier League following his impressive season, but agent Michael Moses does not expect the 25-year-old to end up at the London Stadium.
"It is very unlikely that Danjuma will go to West Ham. Issues related to personal terms, which have not gone well," Moses explained to Spanish outlet Cadena SER.
Danjuma's contract at La Ceramica still has another four years left to run, and the Netherlands international was also tipped to head for Liverpool before the Reds struck deals for Fabio Carvalho and Darwin Nunez.