The former Lazio captain is available from Besiktas this summer.
Sky Italia says Bologna have made contact with Immobile, 35, about a return to Italy.
Besiktas are willing to do business, though Immobile's contract demands could prove a stumbling block.
In the Süper Lig, the former Borussia Dortmund striker scored 15 goals in 30 matches last season.
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