Italian media said Juventus would sign the 28-year-old on loan for two million euros with an option to buy him at the end of the season.
Juventus, Italian champions for the last five seasons, are four points clear at the top of Serie A, yet have still faced criticism for performances that have fallen short of what is expected from potential Champions League winners.
Coach Massimiliano Allegri was seen angrily remonstrating with club officials on the pitch after they lost on penalties to AC Milan in the Italian Supercup on Friday in Doha.
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Miralem Pjanic has not had the expected in impact in midfield since he was signed from AS Roma in the close season.
Rincon has been a regular for Venezuela since 2008 and is playing in his third World Cup qualifying campaign. He is in his third season at Genoa, having spent the previous five at Bundesliga side Hamburg SV.
(Writing by Brian Homewood in Berne, editing by Meil Robinson)
