Reina spent last season on-loan with Napoli.
"I have a contract to respect with Liverpool. I'm training well and I am perfectly fine with my team-mates," the 31-year-old Reina told Cadena Ser.
"I am here to stay. I have not talked to Brendan Rodgers, I've been here for only four days and I am just thinking of training to my best and getting back into shape.
"At the moment all the big Spanish teams are covered in my role, so I see it as very difficult to return to Spain.
"It's normal though that over the years you want to return to where you came from, so we'll see.
"It's amazing that 10 years later I am still away from Spain and that it was he who brought me to Napoli last year."
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