Tuilagi has endured a torrid time with injuries but thankfully his latest pectoral problem was just a strain picked up against Wasps last month.
Fellow England international Youngs suffered a knee injury in the Red Rose's Six Nations opener against Italy and he was expected to be out for the remainder of the season.
Speaking about Tuilagi's fitness, O'Connor feels the centre is making good progress from his knock and, like half-back Youngs, he should be back in the thick of the action soon.
"It should be a couple of weeks rather than months," he said.
"That's hugely positive. He [Tuilagi] is running around and is probably going to be into some team training late end of this week or early next week."
O'Connor added: "Youngs has worked incredibly hard to get back, so that he can contribute at the back end of the season. All the indicators are that he should be in and around selection next week."