Bristol City could face a battle from Standard Liege should they opt to pursue the 24-year-old's signature.
The Finland international, who scored twice in his country's 3-0 win against Estonia this week, is out of contract next summer and has so far resisted the Greek giants' attempts to keep him beyond the end of his deal.
However, the report claims his situation has also alerted Belgian side Standard Liege, whose interest is said to be more pronounced than that of Bristol City.
According to DH.be, Lod's departure is inevitable and could even take place in January, with Panathinaikos plagued by financial problems, and a fee of €500,000 [around £440,000] may be enough to prise him away.
Lod, 24, can play anywhere across midfield, although his preferred role is through the middle.
Bristol City are currently fourth in the Championship, and the chance to play Premier League football next season could convince Lod about a move to Ashton Gate, should an offer come in from Lee Johnson's team.
Would Lod be a good signing for Bristol City?