Coutinho spent five years at Liverpool before joining Barcelona in January 2018, helping them win two LaLiga titles. The pair's time at Barcelona did not overlap as Neymar left the Spanish side for Paris St Germain in August 2017.
Santos shared a video of Coutinho's arrival, showing him entering the dressing room and being welcomed by Neymar.
"If it's a dream, I don't want to wake up," Neymar told Coutinho in the video.
The pair have never played together at club level.
Coutinho, who made his last appearance for Brazil in March 2022, returned to his boyhood club Vasco da Gama in 2024 but left the team in February this year.
Neymar, 34, returned to Santos last year. He announced his international retirement after Brazil's exit from the World Cup in July.