The 26-year-old midfielder has represented his country on four previous occasions, but has found himself in the international wilderness over the last 12 months.
A lack of regular first-team football at Tottenham Hotspur was largely responsible for his omission from the Three Lions ranks, but a summer switch to the KC Stadium has put him firmly back in the spotlight.
Livermore told the Hull Daily Mail on Huddlestone's claims to a call-up for the final round of 2014 World Cup qualifiers: "I don't think there's been too many English midfielders in better form than Tom so far this season so, if it was up to me, I'd be pushing for him to be involved.
"Tom's been fantastic. Saturday's performance (against West Ham United) was one of the best I've seen in the Premier League.
"It was great to play alongside him, as it is every week. Against West Ham, his calmness on the ball, his range of passing and his work-rate were fantastic."
Tigers loanee Livermore has England ambitions of his own, having made his senior bow against Italy in August 2012, but admits it may be too soon for him to be knocking on Roy Hodgson's door.
Asked if he is hoping to be invited back into the fold in the near future, the 23-year-old added: "I wouldn't have thought so. I'm just enjoying my football here at the minute. This is my bread and butter, so I'm just looking forward to the next game.
"If I get a call-up, then great, but if not, I'll keep working hard for the team and see where that takes me."
Meanwhile, Hull's head of medical services Rob Price has announced that Robert Koren and James Chester have made positive starts to their respective recoveries from foot and hamstring problems.
He told the club's official website: "With injuries, it isn't always black and white and you have to see how people progress.
"When we say it could be eight weeks, that doesn't necessarily mean that it will be eight weeks because we always hope we can get them back a little bit quicker than that.
"Robert is doing particularly well with his rehab and we're hopeful that within the next three weeks he could be back out there with the team.
"With James, he has some damage to one of his hamstring tendons and you have to really give that a couple of weeks to settle down for it to start to form some scar tissue before we can start loading him.
"But he's doing well in the early stages of his rehab and, again, he's also working on some other areas. Hopefully in around 10 days we'll be able to start pushing him a little bit more."