The England midfielder dislocated his shoulder in October and was initially ruled out until the end of December, but boss Paul Lambert confirmed he had made his tentative first steps back as he was preparing for Sunday's clash with Leicester City.
Delph's form at the start of the season was enough to earn him a call into Roy Hodgson's England squad, and he has been badly missed by his club, who finally ended a nine-game winless run when they beat Crystal Palace 1-0 on Tuesday.
Lambert, who is also waiting on Philippe Senderos and Ron Vlaar coming back to training, said: "Fabian's coming on, he trained with the team today. It's non-contact at the minute but he's doing really well.
"Ron will maybe do a bit of training on Saturday with the team, he's more advanced than Philippe. He's coming on. I'd like to think we can get into the new year with both of them back.
"That's the target, though we can't put too much pressure on them. And if things go well with Philippe, maybe we can get him back by the end of the month. Slowly but surely we're starting to get guys back."
Lambert has been coming under pressure from fans, not for the first time since he took over at Villa Park, but he insists the club is not in for another relegation battle and things are not as bad as some seem to feel.
He added: "We're sitting 12th at the moment, two points behind Everton, who had a massive season last year, so it's not all doom and gloom. It's the media who portray that.
"We are where we are. We had a hard run of games but we're undefeated in the last four matches and they've been tough, tough games for us but we're slowly but surely getting there."