Dutchman Van Dijk, who joined the club from Southampton in January 2018 for a reported 75 million pounds, has become the lynchpin of a Liverpool defence that has kept a league-high 16 clean sheets this season.
"If the season ended tonight, I would give him it personally," Robertson told British media.
Since its inception in 1974, a defender has won the prize only five times, with former Chelsea captain John Terry the last one to do so in 2005.
"The attacking players are usually in the running because they take all the goals and the headlines but this season Virgil has been fantastic and he's getting all the plaudits that he deserves," Robertson said.
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"He's so consistent as well. If he puts the performances as he has done, there's no reason why he shouldn't have that trophy."
Table-toppers Liverpool, who hold a one-point advantage over nearest challengers City, visit local rivals Everton on Sunday.
(Reporting by Hardik Vyas in Bengaluru; Editing by Amlan Chakraborty)
