Leuluai is the only player unavailable to take on Scotland in their quarter-final at Headingley on Saturday morning (NZT) but the Kiwis weren't taking any risks with a handful of other players who sat out training overnight.
Sonny Bill Williams (shoulder and flu), Manu Vatuvei (knee), Josh Hoffman (shoulder) and Frank Pritchard (knee) skipped training but were all precautionary.
"Where we are at this stage of the tournament, there's no point taking risks with these guys at the start of the week," Kiwis manager Tony Iro said. "Apart from Thomas, I expect everyone to be available [to play Scotland]."
Few expected Scotland to get this far in the tournament, with most predicting Tonga to emerge from Group C. Scotland are undefeated - they beat Tonga (26-24) and the US (22-8) and drew with Italy (30-30) - but realistic about their chances against the defending world champions.
"It will be a tough game obviously, but it's amazing that we've made the last eight of the World Cup," Scotland halfback Peter Wallace said. "The Kiwis aren't super-human. They're a good team but it'll take a massive effort to beat them.
"We'll do our best and give it our all and see where that takes us. We've got nothing to lose and it will possibly be the last World Cup game of a few of the boys so it will be a special occasion for us."
Wallace is one of three NRL-based players in the Scotland squad, along with Titans prop Luke Douglas and Cowboys centre Kane Linnett.
He will return to Penrith next season after six years with the Broncos, where he will come under the watch of coach Ivan Cleary who has been impressed by the Bravehearts at this tournament.
"They haven't lost yet so are very committed and look like the play for each other," the Kiwis assistant coach said. "It's going to be a tough game. For us, it's about getting better ourselves. If we can improve on what we are doing, hopefully that's enough."
Cleary was later due to visit Cameron Ciraldo in hospital after the Italy and Panthers second-rower suffered a lacerated pancreas in a thunderous tackle by Tonga and Warriors centre Konrad Hurrell yesterday. Ciraldo will remain in the UK and is expected to have surgery.
The Kiwis will name their side to play Scotland on Thursday morning (NZT), with most interest around the makeup of their four-prop rotation.