The breakdown in negotiations has attracted the interest of several big clubs such as Real Madrid, Bayern Munich and Paris Saint-Germain, among others.
They claim that he will jet to Italy this weekend to undertake a medical, before signing the necessary pre-contract agreement.
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.
It will however make him Juventus's second-highest earner behind Cristiano Ronaldo, but ahead Paulo Dybala and Douglas Costa.
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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.
Soon after Emery was appointed last summer, it was reported he wanted to build the team around Arsenal's longest-serving player, who was named as one of five captains for this season.
"We need his performances for us and the last matches I am very happy with him".
But it became clear that Ramsey's desire to play as a number eight, running on to the ball from an advanced central midfield position, clashed with Emery's vision.
"I asked him in the last match at Blackpool if he's ok to help us play, he said yes I want to play".