The Turkish winger has been out with a knee injury since August, with Boro losing three games out of four in the period of his absence.
Southgate declared how important Tuncay is for his side, but remains hopeful the 25-year-old could make his comeback against Chelsea next week.
"It's a possibility. He's progressing very well. I think any team would miss a player of his ability, enthusiasm and character," he told the club's official site.
"He's been missed within the group but he's working incredibly hard and he's training with us now."
Playing Football
The Boro tactician is ready to reinstate the former Fenerbahce ace in the team's starting line-up immediately.
"He doesn't enjoy sitting in the physio's room and working in the gym. He wants to be playing football and he will be as soon as he's available," added Southgate.
Southgate used Tuncay as a center-forward behind striker Afonso Alves at the start of the season, but Egypt striker Mido was given the nod during Tuncay's absence.