Livermore has been outstanding with Hull this season.
He told the Hull Daily Mail: "I've really enjoyed myself here. Whatever happens in the summer, whatever the two clubs agree, if they could sort something out that would be great.
"Of course I'd like to stay. I feel as though I owe the manager, his staff, my team-mates and the fans a lot.
"They've been good to me this season and I've been given the opportunity to play week in and week out. For that, I'm thankful. I've enjoyed my time here and I'd like more of the same."
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