It is not the first time Barcelona have been linked with the player, and Mundo Deportivo say that they are looking to sign the attacking midfielder this summer.
Pjanic is 23 and has starred for Roma for the last two seasons in Serie A.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.