The Brazilian playmaker has established himself as a key player at Anfield since his move from Inter in January 2013.
And Liverpool boss Rodgers is hopeful that the 22-year-old will commit his future to the Merseyside club in the not too distant future.
"I am not sure when it will be done," he said after Monday's Champions Cup final defeat against Manchester United.
"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.
"I am sure I will hear more about it when I get back [from the United States] on Tuesday."
Rodgers is expected to make Atletico Madrid defender Javi Manquillo his latest signing on Tuesday.
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'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
