Reina has been linked with a move away, with Arsenal and Barcelona among those interested in him.
"He's never been unsettled and our relationship is very strong. I have given him and a few of the senior boys real responsibility and I think they have enjoyed that. I see him as someone who is going to be here [next season]," said Rodgers.
"He is 30 years of age and is someone who looks after his body. The sports science team this year have worked really well with him. I think he's been outstanding and had great focus and hopefully that will continue for us."