The 23-year-old arrived at the club just after 8am on Tuesday, where it's believed he met with coach Mark Neeld for the first time since his arrest in Alice Springs last week.
His session began on an exercise bike, accompanied by a member of the Demons fitness staff, but he was not expected join his teammates for training outside.
Meanwhile, Green said before training he had "no doubt" Jurrah would return to play football, but admitted his teammate remained a long way from being fit enough to compete at AFL level.
That conditioning process began at training, but Green said Jurrah needs to virtually complete a pre-season and would be expected to do six or seven weeks of solid training to get his body and mind right before he would be considered for selection.
Neeld suggested on Saturday night it might be mid-year before Jurrah came into calculations.
After speaking to Jurrah at training, Green said his "resilient" teammate is very focused on returning to football.
"I just went into the changerooms, saw Liam there (and) said 'how are you going' (and) he said 'yeah, I'm good,'" Green said. "He's looking forward to getting into training."
Green said he expects the Melbourne coaching staff and leadership group to discuss with Jurrah what was expected of him when away from the club, as well as aspects of his time in Alice Springs.
"The hierarchy will speak to him at some stage today and go through a process of getting Liam right to play football," Green said. "That will be an all-encompassing conversation."
Green added Jurrah would not enjoy being the centre of extensive media focus.
"I'm not saying Liam can't cope with it because he can, he's a big boy, but I'm saying that with the focus that has been on Liam .. he just wants to get out and play footy," said Green.
"We all would not want the focus like that on any of us."
Green would not be drawn into the discussion around Fox Footy and Collingwood president Eddie McGuire's interview with Jurrah on Sunday night, although he said from a player's perspective he would hope protocols would be followed.
Jurrah was charged with two offences following an alleged machete attack in Alice Springs last week.
He was granted bail and denied any involvement in a fight that broke out at a local town camp near Alice Springs.
Jurrah is battling a wrist injury on top of his personal woes. It is not clear if he'll return to the Demons line-up ahead of his scheduled court appearance in Alice Springs in May.
