The 28-year-old Wales worldwide had already been told by new Arsenal manager Unai Emery that he did not feature in his plans at the Emirates and will soon bring to an end his 10-year association with the north London club.
Earlier this season, the Gunners announced that the club would not be offering the Welshman a new deal so an exit has always looked likely. Ramsey will be the club's second highest paid player after Portuguese striker Cristiano Ronaldo (€ 31 million per year).
However, according to Sky in Italy, terms have now been agreed between the two parties and Juventus will finalise the transfer during the middle of next week.
Ramsey was said to be keen to stay yet grew frustrated with the protracted process and, by the end, there were doubts over whether he would have put pen to paper.
Meanwhile, head coach Unai Emery had reservations about Ramsey's role in his squad.
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The Wales global is Arsenal's longest-serving playing, having moved to the Emirates from Cardiff City as a teenager back in 2008.
"In the last match I was very happy with him".
"His future is individually for him, for his family, his agent".
"I want his behaviour and his focus to be on West Ham on Saturday".
The report says Ramsey's "boyhood dream" was to play for Barcelona but after preliminary talks he will not be moving to the Nou Camp.