Kagawa, 31, is currently without a club after leaving Spanish side Real Zaragoza this month.
And according to Sportime, he is a concrete target for PAOK who can sign free agents until October 23.
The Greek club are ‘pessimistic’ about their chances of signing Kagawa, believing he will receive offers from bigger leagues.
However, they are trying to convince the Japan midfielder to wear the black and white shirt of PAOK.
Kagawa made a name for himself in Europe with Borussia Dortmund, having two spells with the Germans either side of two years at Man United.
Following a loan stint at Besiktas in 2019, he signed for Segunda División side Zaragoza on a two-year deal.
Kagawa made 36 appearances in Spain last season, but agreed an early contract termination this month.
He expressed disappointment at having to leave, a decision that may have been financial as he was a top earner at Zaragoza.
Kagawa would favour a Spanish stay, with local media reporting Sabadell as one of the clubs interested.
Now one of numerous high profile free agents on the market, it remains to be seen if PAOK can lure Kagawa to Thessaloniki.
He would be joining a side currently doing well in the Greece’s Super League. PAOK are second after four games, two points behind leaders Aris.