Livermore has featured in all but two of Hull's Premier League games in 2013-14 and helped the Yorkshire club reach a first FA Cup final.
The 24-year-old feels settled at the KC Stadium and is hoping the two clubs can thrash out a deal to enable Livermore to remain part of Steve Bruce's squad.
Ahead of Sunday's final league game of the season at home against Everton, Livermore told TheHull Daily Mail: "Will it be my last game at the KC? I don't think so, no. Or I hope not.
"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."
