Welbeck, 28, broke his right ankle in a Europa League draw against Sporting Lisbon at the Emirates in November.
"He's progressing very well," Emery told Sky Sports.
"He is working and starting to touch the ball and to work on the pitch. His progress with such a big injury is going very well.
"It's difficult for him to play matches this season but he is progressing very well and maybe the doctor will tell us he can come train with us in the last weeks of this season.
"After, his individual thing is to speak with the club [about his future]."
When asked about Welbeck's contract situation at the club, Emery said: "Every [English] team needs English players.
"Danny has his injury now. He was going with the national team and we were happy for him and the national team.
"[Promising English players] are now in [Arsenal's] under-18s, under-19s, under-20s and under-21s teams.
"We have a lot of players with the possibility to grow up with us and be part of our future, and also with the national team."