The Swedish striker has reportedly targeted a return against Tottenham Hotspur at the end of October although boss Jose Mourinho has insisted the 35-year-old will not be rushed back into first-team action before the new year.
But reports state he is now jogging without any issues and the club's conditioning coaches expect him to receive the green light during the next fortnight to start working with the ball again on a daily basis.
They have also pointed out the Red Devils are poised to name the giant hitman in their submitted Champions League squad in the coming days, even though the final group game takes place in early December.
Mourinho clearly does not want to heap unnecessary pressure on the veteran as he continues to make giant strides from the knee operation he underwent back at the beginning of May.
But the sight of the former Paris Saint-Germain forward being able to perform shooting drills will only add to the belief he will be back among the main group soon.