The Spain international has spent the 2013-14 campaign with the Serie A side after his parent club signed Belgian shot-stopper Simon Mignolet from Sunderland in the summer.
Reina recently declared that his future is uncertain amid rumours of a possible return to Spanish champions Barcelona, with whom he started his career, although he remains under contract at Anfield.
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"He wrote a goodbye letter didn't he?" Rodgers said.
"Obviously Pepe made it very clear when he went to Napoli that he was looking to move because he penned a great big letter saying he was going to work with the best manager that he'd worked with (Rafael Benitez) and thanked him for his time for Liverpool.
"So, for me, it probably sounded like he'd made his decision there."
Meanwhile, Rodgers has urged his entire team to take more defensive responsibility after witnessing them concede three goals in the dramatic 4-3 win over Swansea City last weekend - a result which means, of sides in the top half of the table, only Newcastle have conceded more.
"Defending is about everyone, it's not just the back four and the goalkeeper," he continued.
"We didn't defend well enough as a team last week. We didn't press the ball well enough at the top of the field.
"We didn't keep the ball well enough, we didn't make enough passes. It was more a collective issue than any individual. We need to defend better as a team.
"This is a team which is evolving and improving all the time. It was a huge task when I came here to improve our goal scoring and that's something we've done. As this team grows we will improve in other aspects."