The Scotland captain, in the final months of his current deal, has lost his first-team spot to £40 million summer transfer window signing Milos Kerkez.
But 31-year-old left-back Robertson has still made 20 appearances so far this season.
"It's a difficult question to answer. I've got five months left, and we need to see the option to stay or if there are options to go," said Robertson, who has won eight major trophies since joining the Reds in 2017.
"I need to see what myself, and my family, want moving forward. I've given absolutely everything for the club for the last eight-and-a-half years, and the club have been very good to me.
"They have rewarded me with good contracts when I have been playing well. My relationship with the people higher up in the club has always been excellent since the day I came in."
He added: "Signing me for £8 million (from Hull) and then doing what I have done helps that - I remind people of that all the time!
"The relationship is good, and it's not quite 'what do they need to show me and what do I need to show them' as we've shown each other more than enough respect over the last eight-and-a-half years and we'll see what comes."
Robertson could have moved to Atletico Madrid after helping Liverpool win a second Premier League title in five years, but stayed in the knowledge that the 22-year-old Kerkez might take his place.
But Robertson insisted his desire for first-team action remained undimmed.
"I think Jurgen Klopp left me out of one game and I was raging, so I'm a player who wants to play," said Robertson, who may be back on the bench for Saturday's visit of Burnley.
"I've played through injuries, I've played when I've only been 50, 40, 30 per cent fit for this club and my country.
"I do have a different role here this season which I'm getting enjoyment out of but at the end of the day, footballers want to play, and if anyone is sat happy on the bench then they don't belong at any football club."