JESSE Hogan is back training with Melbourne and appears set to take his place in the Demons' side against Hawthorn at the MCG on Sunday.

Hogan was granted compassionate leave by the Demons following the death of his father Tony late last week.

The star forward did not play against Essendon on Sunday and travelled to Adelaide to be with his family over the weekend, and to attend his father's funeral.

Coach Simon Goodwin was due to speak to Hogan on Monday night, with the Demons adamant they would not place any pressure on the star forward to return before he was ready.

Hogan returned to the club on Tuesday and joined teammates for a light jog around Gosch's Paddock.

A decision on whether Hogan will play is due to be made later in the week, but the Demons are leaving the call in his hands and will not rush his return. 

Melbourne's main training session is set for Thursday and Hogan is set to join teammates on the track ahead of the game against the Hawks on Sunday. 

Hogan has kicked six goals in three games, but was suspended for two matches for striking Carlton's Sam Rowe in round two.

The star forward was caught smoking at a music festival in Perth after Melbourne granted him a three-day leave period to visit his family and his father, whose health had deteriorated over the past few months.

Although not condoning Hogan's actions, Melbourne said at the time it would continue to support the star forward during a difficult period.

Goodwin said on Sunday that Hogan's wellbeing was the club's first priority. 

"As we've said all along, it will really be up to Jesse. He's obviously going through a lot. His welfare is first and foremost for us, but we'll get more of a guide early in the week," Goodwin said after the win against Essendon.