Reds legend Gerrard recently replaced Dean Smith as manager at Villa Park.
He will return to Anfield to face his former club on December 11.
Speaking about facing Klopp, Gerrard said: "I've been in touch with Klopp, I bump into him when he walks his dogs.
"He sent me a message saying he is 'looking forward to a big hug on the side' when Villa play Liverpool next month."
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