The 23-year-old starred as the Lisbon-based side won the Primeira Liga this season, making 35 appearances in all competitions.
And John is now expected to sign a five-year deal with the Swans once the Welsh side agree a transfer fee with Benfica.
"It has always been a dream of Ola's to play in the Premier League," Collins John, the former Fulham striker and Ola's brother and agent, told Voetbal International.
"Some other clubs in the Premier League were interested, but Ola had the best feeling with Swansea City.
"Last season Swansea already tried to sign Ola, but the transfer failed at the very last moment. The club followed him after that in the hope of agreeing a contract with him. That moment is very close."