Juve have been trailing Can since last summer, where Liverpool told them to surrender their interests.
Can has refused the contract Liverpool have offered him and the German is expected to head to Turin at the end of the campaign.
And Corriere dello Sport’s report, which names United as a transfer rival to the Old Lady, claim Juve are considering moving for Can now rather than risking it for the summer.
To do that, it is claimed, they will need to offer Liverpool a £5.3m transfer fee.
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Corriere dello Sport claim Man Utd are also keen on Emre Can
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That strikes as a bargain price for a player widely regarded to be worth many times more.
Liverpool are very unlikely to accept any offer from United for Can, so Juve could get some success at the negotiating table if they are the only other option.
Asked about signing Emre Can in January, Juve boss Max Allegri said: “We have 21-22 players and the core is of quality.
“I have not asked for any reinforcements because then we will have too many and I’ll have too much chaos to think about.
“I’m happy with this team, the important thing is not to lower the tempo.”