Liverpool are in talks with Tottenham about a deal for the veteran left-back.
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But Van Dijk, after defeat at Bournemouth on Saturday, said: "He's my vice-captain.
"Robbo is a very important member of our team and I want him to stay but whatever happens, let's see."
Asked if he expects Robertson to leave this week, Van Dijk also said: "That's not on me, is it?"
The Liverpool skipper was then asked about his best memories of Robertson but insisted he would only "speak about that" if the move happened.