Conan, 31, has not played since hurting his foot in a warm-up victory over Italy on 5 August.

Dave Kilcoyne, Rob Henshaw, and Dan Sheehan, on the other hand, could face Tonga after fully training on Wednesday.

However, Ireland squad manager Mick Kearney believes it will be too soon for Conan.

“Very good training session today, everybody came through that really well,” Kearney added.

“Jack was out running, which was a real positive, and while Saturday will come a little early for him, I think the signs are really positive in terms of being able to train fully next week, and hopefully he will be able to compete in South Africa.”

“This is his first [time on the training pitch] in a few days.” He has spent the majority of his rehab time in the gym with the physios.

“Obviously, it was a significant day for him in terms of getting out and running. He ran really well, which is quite encouraging, and he was in a good spot afterwards.”

When questioned about prop Kilcoyne’s hamstring injury, center Henshaw’s hamstring injury, and hooker Sheehan’s foot injury, Kearney said, “They were all integrated fully into training today, and all trained fully, so that’s positive as well.”

Andy Farrell, Ireland’s head coach, will pick his team to face Tonga in Nantes on Thursday afternoon.

On Saturday, Ireland launched their World Cup campaign with a 12-try thrashing of Romania in Bordeaux, with captain Johnny Sexton scoring two tries on his comeback.