Lazio president Claudio Lotito wants Pedro to play on next season.
This season, the Spanish winger, now 39, has scored twice and assisted a further two goals in five games across Serie A and the Europa League.
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Il Corriere dello Sport says Lazio will offer Pedro a new contract until the summer of 2026.
The former Barcelona and Chelsea attacker joined Lazio from local rivals Roma in the summer of 2021.
He has since made 137 appearances in the light blue shirt.