After joining from Toulouse in January last year, the 21-year-old became a first-team regular for Monchengladbach in 2021-22, scoring three goals and registering one assist in 29 appearances across all tournaments.
The likes of Manchester United, Leicester City, Atletico Madrid and Juventus have all previously been credited with an interest in the Frenchman, who still has three years remaining on his contract.
However, L'Equipe claims that Newcastle have joined the race for his signature and they are ready to submit an offer in excess of €35m (£29.5m) for the midfielder.
Monchengladbach have no plans to sell Kone this summer and they regard the France Under-21 international, who they signed for just £8m less than two years ago, as an invaluable first-team asset.
Eddie Howe has a number of midfield options already at his disposal, including Bruno Guimaraes, Joe Willock, Joelinton, Sean Longstaff, Matty Longstaff and Jonjo Shelvey, the latter of whom, however, is sidelined for the next few months with a hamstring injury.
Another midfielder on Newcastle's radar is Los Angeles FC's Jose Cifuentes, with both the Magpies and Leeds United reportedly joining Brighton & Hove Albion in the race for his signature.
The Seagulls are believed to have expressed their interest in signing the 23-year-old this summer in a deal worth around £6m.
However, The Sun claims that they are set to face competition from both Newcastle and Leeds, with the Premier League pair desperate to pip Brighton to sign the Ecuador international.
The report adds that Cifuentes missed out on a move to the English top flight two years ago, but the midfielder now qualifies for a work permit as a senior international.
Cifuentes has impresses in the MLS with LAFC since joining the club in 2020, scoring 13 goals and providing 15 assists in 84 games across all competitions.
The midfielder could become the fourth Ecuadorian to play for Brighton should he decide to link up with Graham Potter's side, who already have Moises Caicedo, Jeremy Sarmiento and new recruit Pervis Estupinan on their books.
Staying with Brighton, Potter has confirmed that centre-back Matt Clarke is set to join Championship outfit Middlesbrough on a permanent deal.
Manager Chris Wilder is keen to recruit a left-sided central defender before the transfer window shuts on September 1, and has identified 25-year-old Clarke as one of his top targets.
Sky Sports News claims that Boro have agreed a £2.25m deal with the Seagulls to sign the defender, who will undergo his medical within the next 24 hours.
Speaking at a press conference on Tuesday ahead of Brighton's EFL Cup clash with Forest Green Rovers, Potter said: "It's a good opportunity for Matt. He gets a chance of more regular game time. He has been fantastic to work with, I must say.
"A great character so, if it happens, Middlesbrough have got a good player there, a good person, so it's good for everybody, I think."
Clarke has not made a single senior appearance for the Seagulls since joining the club in 2019, and spent last season on loan with West Bromwich Albion, making 33 Championship appearances.
Elsewhere, Nottingham Forest are reportedly interested in signing Atalanta BC's right wing-back Hans Hateboer.
The Tricky Trees have already raided the Serie A club for midfielder Remo Freuler this summer, with the 30-year-old moving to the Premier League after six-and-a-half seasons with La Dea.
Calciomercato claims that Forest have set their sights on luring 28-year-old Hateboer to the City Ground, and there is optimism between both clubs that an agreement can be reached.
Since joining Atalanta in 2017, Hateboer has made 196 appearances for the club across all tournaments, scoring 10 goals and registering 19 assists.
The potential arrival of Netherlands international Hateboer at Forest would see him become Steve Cooper's 17th signing of the summer window.