Leinster's Garry Ringrose, James Ryan and Hugo Keenan appear to be winning their race to be fit for the Investec Champions Cup final against Toulouse in just over two weeks.
The trio all missed out on both the Champions Cup quarter-final win over La Rochelle and the semi-final victory over Northampton Saints at Croke Park last week, with Ringrose sidelined with a shoulder issue, Ryan rehabbing an arm injury, and Keenan out with a hip problem.
All three miss out again for tomorrow's BKT United Rugby Championship meeting with the Ospreys, but Cullen is confident that some of them could get a run out in next Saturday's trip to face Ulster in Belfast.
"They're going pretty good," Cullen said of his injured co-captains and Keenan.
"Again Garry [Ringrose], as I said to you last week, I thought he would have been involved last week, but again he just had a bit of a setback during the course of the week. We’ll see how that settles down really. I don’t think it is anything major. He got to the stage where he was very close to playing.
"Hugo [Keenan] hadn’t quite done enough, but he’s back running fully now. Hopefully he’s pretty close.
"Similar with James [Ryan], he’s pretty close now as well. It’s down to what is the exact right game to put them into.
"It’s not this week, but I think hopefully we’ll see a few of them in action next week. We’ll see, it’s day-by-day."
The Leinster coach has named a strong team for Saturday's return to URC action against the Ospreys at the RDS.
Will Connors comes into the side among five changes from their win over Northampton last week, with 14 of the starting 15, and 19 of the matchday 23 having featured at Croke Park a week ago.
Having fallen to second in the URC table with three rounds to play, the province can't afford to take their eye off the ball if they want to secure one of the top seeds for the business end of the season.
And Cullen is expecting a fired up Ospreys to arrive in Dublin, with Toby Booth's side hunting down a spot in the play-offs, along with Champions Cup qualification.
"We're in the situation we find ourselves in the URC, that's a very important piece for us so we want to make sure we give ourselves the best chance.
"Ospreys are a very formidable opponent as well. The Welsh regions have had their challenges over the course of the season but the Ospreys have come through and found some good form. We know a lot of their players over the years and they have a doggedness about them. We need to make sure we prepare well for that this week.
"Even under the stands last week in Croke Park, our minds are naturally turning back to the URC because we need to take care of the bread and butter, the mainstay of our season. We need to make sure we try and get a decent seeding.
"We lost ground on the South African trip, let's call a spade a spade. We lost ground with that trip. We would have hoped we went a little bit better than we did, and that's why we find ourselves behind Glasgow currently in second, versus when we departed these shores, we were sitting in a slightly better position," he added.
Leinster have continued their rollout of contract announcements this afternoon, with Cian Healy the latest player to be confirmed on their squad next season.
The 36-year-old, who is rested tomorrow, is just five appearances short of Devin Toner's record of 280 for Leinster, while he's also just four behind Brian O'Driscoll's record of 133 Ireland caps.
And Cullen paid tribute to the loosehead's longevity.
"He was playing with me for quite a few seasons. That just shows you how old he is," Cullen joked.
"He is an incredible person, Cian. He really is remarkable and he's just so authentic.
"As I’ve talked about in the past, he was great to play with. I had seen him come through as a younger player, trying to help him along the way, whether that helped in any way or not. I doubt it!
"It is great that he has agreed to sign on, and he has added strings to his bow as well over the course of his career.
You see him in the Six Nations game [against Scotland in 2023], where he comes on and plays 40 minutes at hooker. He has played games for us as a tighthead as well. For him to be able to do that and have the mindset to do that, is hugely attractive. For an experienced player in the group to be able to do that so comfortably is great for us to have.
"We’re delighted that he has agreed to stay on. It was nice in the dressing room the last day where he becomes the record cap holder in the Champions Cup tournament. He’s a pretty special individual."
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