Ramsey is out of contract with Arsenal at the end of the season.
The club have withdrawn the offer of a new deal meaning that he is likely to leave.
The Wales international is a target for Juventus but they will only move for him if they cannot land Rabiot.
The France international has rejected four offers of a new deal from French giants Paris Saint-Germain.
Juventus are locked in a battle with Barcelona and Liverpool for Rabiot and will only enter the bidding for Ramsey if they lose out.
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Ramsey isn’t going to be short of offers, however, with AC Milan, Chelsea, Manchester United and Liverpool all keeping tabs on him during this season.
Juventus picked up a high-class free-agent in Emre Can last summer, and are open to another similar transaction with Ramsey.
It is thought that Liverpool are extremely keen to land the 27-year-old, with reports in Italy suggesting they will deliver what Arsenal could not.
Ramsey was bargaining for a much-improved deal with Arsenal that would make him one of the club’s top earners, alongside Mesut Ozil.
The German playmaker earns £300,000-per-week compared to Ramsey’s £110,000.
Ramsey explained his dismay at the impasse in negotiations this week, saying: “Everything has been going great with the club – we thought we were in a position where we had agreed a deal but that’s no longer the case.
“So I just have to carry on playing my football and do my best for Arsenal this season and I’ll leave the rest with the club.
“Am I disappointed? That’s a decision they have made and things happen in football and you just have to get on with it.
“That’s all I am concentrating on and giving my best for Arsenal.
“Would I stay for the rest of the season? Of course, yeah.
“I am contracted to Arsenal and I am going to do my best to try and achieve something special.”