Arriving at his new base last week, with both Super Rugby and Mitre 10 Cup titles, in his armoury, Taufua has been signed by Leicester to increase its ball carrying options among its pack.
Tigers coach, former Ireland international Geordan Murphy, told leicestermercury.co.uk, "Jordan has played a lot of rugby this season, so we will see how he goes and manage him through the week.
"But, he's settling in well and began training with the squad this week, so if we feel he's ready to go we will include him.
"He has obviously been involved with the Makos. He was a champion with the Crusaders and then he has gone to the Makos who won their competition last weekend.
"It's important to get guys like that involved. He is going to be a huge person for us in the squad.
"He's a winner, he's got huge experience," Murphy said.
"I'm expecting big things from him and I want to try and get him involved in the team as quickly as possible really.
"The balance for him is a little bit different. We'll look after him, try and get him integrated into the group and it's likely he'll travel with the squad away to London whether selected or not to play," he said.
Getting Taufua involved, along with fellow new signing Argentine lock Tomas Lavanini, would help cover for the six members of the side who played for England at the World Cup.
They are expected to have a break before returning to action for the side. Leicester play London Irish this week and it was more likely returning players would be considered after that, he said.