The Italian goalkeeper will leave the Old Lady at the end of June after making 14 appearances for Andrea Pirlo's side in all competitions this season.
It is believed that Buffon, at the age of 43, is looking to continue his career past his next birthday and he wants a regular starting role with his next club.
The Daily Mail reports that the Portuguese side Benfica are keen to sign the veteran goalkeeper, with the club able to qualify for the Champions League next season.
Buffon has a decorated personal trophy cabinet, having won 10 Serie A titles, the Ligue 1 title once and the World Cup with Italy, but a Champions League medal still eludes the keeper after three final defeats.
The 43-year-old has in total spent 19 years with Juve across two spells and has made 930 club appearances across his whole senior career, which started in 1995.