Tottenham midfielder Livermore joined Hull on a season-long loan deal in the summer after finding himself down the pecking order at White Hart Lane.
The 24-year-old has impressed at the KC Stadium and Tigers boss Steve Bruce has intimated he would be keen to keep Livermore on a permanent basis.
Livermore has settled into life at Hull and he admits it is up to the two clubs to discuss his long-term future.
"I'm still a Tottenham player so I don't know the situation at the minute," Livermore told the Hull Daily Mail.
"As far as I know, Tottenham seem to be coping without me so I don't see any reason why there would be a recall.
"In the meantime I'm happy here playing my football with Hull. If the two clubs could sort something out I'd be more than happy to look at it.
"I've been here long enough to know what the club and the manager are about so I'd be more than happy to listen to any interest.
"I love the area. I've moved into a new place recently. It's nice and quiet and pretty much how I lived just outside of London.
"It's a nice place to be, for my whole family, not just myself, and nice to be playing football."