The 24-year-old midfielder, having been deemed surplus to requirements at White Hart Lane, was allowed to link up with the Tigers last summer.
He has become an integral part of Steve Bruce's plans alongside Tom Huddlestone - another to have made the journey north from Spurs - and is thoroughly enjoying his football.
A return to the capital was mooted in the New Year, with Tim Sherwood having succeeded Andre Villas-Boas as Spurs boss, but Livermore made it clear to his parent club that he wished to honour an agreement with Hull.
He told the Hull Daily Mail: "I spoke to people at both clubs and just stressed that I wanted to stay here and play football.
"I think within that, Tottenham allowed me to stay until the end of the season.
"I think it was just something to do with Tottenham wanting to push Hull's arm. With what I said to Tottenham it became apparent it was the best for all three parties for me to stay."
Hull manager Bruce has already expressed a desire to make Livermore's deal permanent in the summer if Spurs are willing to negotiate, and the one-cap England international is ruling nothing out at this stage.
Livermore added: "Long term, I love the squad here. I love everything around here.
"The gaffer's great. I like the way we try to play football. It's a big statement, the players he's signed. To go and spend that money to bring in that sort of quality, it proves which way he wants the club to go.
"For any young player signing, that's a massive boost.
"Personally I still feel like I've got a point to prove. I was in and out at Tottenham and it's not a nice feeling when managers don't come and talk to you and tell you what you're doing wrong or why you don't get the chance you feel you should be given."