Perenara, 29, is contracted to Japanese rugby team rugby team NTT Docomo Red Hurricane, but his deal expires in May.
Having expressed previous interest in switching codes and joining the Roosters, a deal could imminent for the New Zealand star.
Roosters coach Trent Robinson said Perenara’s character and leadership traits is something that the club are looking to bring in.
“His character has been there to see for a lot of people over a long period of time,” Robinson told NRL.com.
“He has captained his club [Wellington Hurricanes], he has played for the All Blacks 64 times and led something very sacred to them, in the Haka, many times as well.
“He has got a big decision to make and it has been great discussing it with them and we will see where it gets to over the next few days. By Monday, I would say, we will know where that is at.”
Robinson added that given the Roosters’ injury crisis in the hooking department, the club would keep their options open on potential inclusions.
“You have got to think about what your team needs and then you think about what are your options available,” Robinson said.
“If you have got a narrow vision on it you are going to come up with limited ideas and rugby union is close to our sport.
“We have obviously had one [hooker] retire and one have a season-ending injury and we feel like the man [Perenara] is a man that we would love to have in the colours so we will see in the next few days.”
Speaking to reporters earlier in the week, Perenara said he believes he can make a smooth transition to league and a move to the hooker position, despite the challenges that come with moving to a new team mid-season.
“I feel the game for a hooker suits the style of game I like to play already in rugby, although knowing that there will be more tackles to be made in league,” he said.
“The fitness – going back and forth 10 metres and getting up off the deck – will be a little bit more compared to rugby so I understand that there will be some conditioning things I will need to adapt to but I do think that I can be successful in the league as well.”
“But it’s something that I don’t think would be the biggest challenge going to the game. I think the time constraint of entering a team later in the year and trying to gel with players and win a championship – that would be the biggest constraint.”