The 26-year-old, who has won four caps for the Three Lions, has not featured since November's 4-2 defeat to Sweden.
However, Livermore believes that the midfielder's form since completing a short-term move to the KC Stadium warrants a spot in Roy Hodgson's squad.
"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," Livermore told the Hull Daily Mail.
"Tom's been fantastic. Saturday's performance was one of the best I've seen in the Premier League. It was great to play alongside him, as it is every week. His calmness on the ball, his range of passing and his work-rate were fantastic.
"People see it as me doing his work for him but he works just as hard. He's got fantastic quality on the ball and that decision-making in possession makes him the player he is."
The pair are on season-long loan deals from Tottenham Hotspur.