Brendan Rodgers' side are second in the Premier League table while Newcastle are currently in 11th place, but could climb back into the top ten with a win on Wednesday.
And while the Magpies have lost their last two matches, Shelvey - who is likely to captain the side with regular skipper Jamaal Lascelles still sidelined with a knee injury - is adamant that confidence remains high among Steve Bruce's players.
"We did really well at the start of December, got wins under our belts and put us on 25 points, then we've obviously lost the last two but we've played very good teams," Shelvey said.
"Man U, it was always going to be very tough going there, but I think the Everton game, we probably deserved a bit more than what we actually got. But I'd say overall, it's been a successful December."
Saturday's loss to Everton was United's first home defeat since the opening weekend of the season, with St. James' Park proving to be a difficult place for opposing sides to visit this term.
And Shelvey added: "We need to just get back to that. After the two results, we need to obviously try and win the game and take the game to them, but we need to stay in that game for as long as possible.
"They'll probably have a lot of the ball - obviously we're not a team that's reliant on possession - but we'll be in the game, there or thereabouts, and hopefully we can get the three points."
Leicester defied the odds to win the Premier League title in 2016, and only the fantastic form of Shelvey's old club Liverpool is keeping them off the top spot this term.
"Liverpool, you don't feel like they're going to lose any game, but regardless of Liverpool, you need to look at what Leicester have done and the team that Brendan has managed to put together," Shelvey said. "They've got some top, top players so it's going to be a tough game.
"It's one that we're looking forward to - and one we feel we can get something out of.
"They've had a little blip of late, but then they go and follow it up with a win at West Ham, so it's going to be a tough game. You need to give them credit for what they've done so far this year.
"With Brendan's teams, he's very much based on possession, keeping the ball and knackering the other team out. I worked with him at Liverpool and he's a fantastic coach, probably one of the best in terms of the tactical side of it on the training pitch.
"You want him to do well - but after tomorrow."
