The bustling back-row forward, who has joined Widnes on a season-long loan from Wigan, missed the start of the Super League campaign after undergoing shoulder surgery in the wake of England's autumn internationals.
Hock, who has been in light training with his new team-mates for a fortnight, will begin full contact work on Wednesday and could come into contention to make his debut in Sunday's derby with St Helens at the Halton Stadium.
"Gaz is very close," said Vikings coach Denis Betts. "He has been given the all-clear by the specialist and we'll bring him into full training this week.
"He's looking really good and I'm looking forward to getting him into the team, but I won't force the issue. We've got him all year.
"We'll look at how he goes this week and make a decision. It would be a big game for him to come into, given he hasn't done any real training."
Betts is also acting with caution over the club's other high-profile signing, stand-off Kevin Brown, the brother-in-law of Hock who was forced to undergo ankle surgery following a training-ground injury.
"Kevin is not far off but there is no pressure to rush him in," Betts said. "He'll play when he's ready, which could be next week or the week after."
Brown would have been an automatic choice to replace Danny Craven, who suffered a broken collarbone in Sunday's opening 28-14 win at London Broncos, but Betts also has the option of switching Rhys Hanbury from full-back and recalling the fit-again Shaun Briscoe.
Centre Cameron Phelps is also available after missing the opening game with a calf strain.
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