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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.