The Uruguayan striker has been linked with a possible summer departure from Anfield with a number of clubs showing interest but new Reds boss Rodgers is supremely confident the former Ajax ace will put pen to a new deal.
"I have had a good conversation with Luis over the phone," Rodgers told the club's official website.
"From the outset, he has seemed a really good guy. He loves the city and the passion.
"We have exchanged lots of texts. He sent me a text on the first morning, wishing me good luck.
"He has really bought into what we are trying to do.
"He was really excited about how we played at Swansea last year. He is really keen and looking forward to playing in a similar sort of model.
"There has been good dialogue (on a contract). I would hope going forward that we can close that out."