The 27-year-old Scotland international underwent operations after last season drew to a close, and while he is nearing a return, he is unlikely to figure in the club's pre-season campaign until their trip to Portugal later this month.
Manager Steve Bruce told the club's official website: "Craig is back training.
"He had a hernia operation three weeks ago, so he will be fine in a week's time.
"I don't think I will play him against Munster or Darlington and he will likely get his first game in Portugal."
The Black Cats will face a Munster XI in Limerick next Tuesday evening, and then line-up against North-East neighbours Darlington at the Northern Echo Arena a week on Saturday before heading for Portugal, where they will play three games.
However, while Gordon may not be involved in Ireland, Andy Reid could be after finally shaking off a calf problem which left him also needing surgery.
Bruce said: "Andy will come with us. He's only played three games since Christmas, which is quite incredible.
"It's an important time for him. He's had one or two injuries - now let's hope he's over it and gives himself the best possible chance."
Only midfielder David Meyler, who suffered a serious knee injury against Manchester United in the Black Cats' final home game of last season, remains on the long-term casualty list.
Bruce said: "David is progressing well with his rehab. He's on course, but it's a long, hard road back for him."