The Brazilian midfielder has been an important part of Chelsea's impressive league form this season.
But Juve hold a long-standing interest in the 23-year-old having missed out on the player when he left Internacional in 2012.
And according to Tuttosport, Oscar has concerns that his playing time may be restricted in the near future.
Juve are said to have sent scouts to watch the player in action for Brazil against France on Thursday night.
And while they appreciate that Jose Mourinho will be very reluctant to let Oscar leave, they reportedly believe the player is open to a new challenge.
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Oscar could leave Chelsea
We are now leading the Premier League and that is our focus.
Oscar
Oscar recently admitted it was tough being knocked out of the Champions League by PSG, by insisted it won't ruin Chelsea's season, saying: "It was very tough for us [losing to PSG]. But Mourinho came to us right after the match and told us to forget about it immediately.
"He said that we had to forget it in the minute after the final whistle and have our minds on the Premier League only.
"So, we got over it. We have won a trophy (the Capital One Cup) already this season. We are in the top spot in the Premier League.
"Obviously we would like to win it all.
"But sometimes we face great opponents as well.
"PSG deserved that victory, no question about it.
"But we are now leading the Premier League and that is our focus."
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