Coutinho has made a big impact at Liverpool since he moved to Anfield from Inter Milan in an £8.5million transfer 18 months ago.
Rodgers views the 22-year-old Brazilian as an important part of his side's's future and he is hoping the playmaker will sign the new deal he has been offered shortly.
"I am not sure when it will be done. I haven't spoken to any of the directors in the last few days so I am not sure where we are on that, but obviously he is someone we want to tie up for a period of time," the Liverpool manager said after his team's friendly defeat to Manchester United in Miami.
"I am sure I will hear more about it when I get back on Tuesday."
Coutinho scored five goals in 37 appearances for the Merseyside club last season.