The Bundesliga club are in the market for a new centre-back after losing both Ibrahima Konate (Liverpool) and Dayot Upamecano (Bayern Munich).
And while Wolfsburg defender Maxence Lacroix is highlighted as their number one target, Leipzig have also been alerted to Norwegian international Ajer.
Steve Bruce’s side were linked with an £8million move for the 23-year-old as he enters the final year of his contract but no such deal has materialised yet.
Ajer wants to leave Scotland this summer with Norwich City and Bayer Leverkusen also said to be keen on his signature.
Newcastle urged to sign ex-Sunderland man
Former Leeds United striker Noel Whelan has urged Newcastle to sign free agent Patrick Van Aanholt.
The left-back, who has started both of the Netherlands’ Group C games at Euro 2020, has ended his four-year spell with Crystal Palace.
The 30-year-old is unlikely to be short of offers, and Whelan believes he is a player Bruce should consider.
Van Aanholt had a short loan with United in 2010, though is more remembered for his time at Tyne-Wear rivals Sunderland.
He told Football Insider: “You have a lot of players out of contract at the moment.
“Look at Van Aanholt. I’m sure he could do a job at Newcastle. He’s someone who can add that quality and experience.
“Newcastle have to be clever in the transfer market and look at players who are out of contract.
“Maybe a two-year contract for some players, Van Aanholt would be one for me. They have to look at him.”
Tottenham Hotspur linked with Ozan Kabak
Ozan Kabak is reportedly wanted by Tottenham Hotspur managing director Fabio Paratici.
The Turkish international remains on Newcastle’s transfer shortlist having almost signed the Schalke defender on a loan-to-buy deal before Liverpool swooped in.
Jurgen Klopp opted against sanctioning a permanent £18m move for the 21-year-old, however, as per Tuttomercatoweb, his Premier League dream may not be over.
Spurs' new director Paratici is an admirer of the player, as are several clubs in Italy such as Roma, Lazio and Atalanta.