All three players have been troubled by calf muscle problems of varying degrees.
Prop Jenkins has not played since January, while fly-half Stephen Jones missed all three of Wales' World Cup warm-up Tests last month after pulling out during the warm-up before facing England at Twickenham.
Back-row forward Ryan Jones, meanwhile, rested his calf when Argentina visited the Millennium Stadium two weeks ago. He would have captained Wales for a record-equalling 28th time.
Wales open their Wold Cup campaign against reigning champions South Africa next Sunday, then tackle a dangerous Samoan outfit in Hamilton seven days later, before facing Namibia and Fiji.
"The word is they are progressing well and are hopefully going to be fit for selection," said Gatland.
"If not for this game, then definitely for the second game."
All three players were named in Gatland's 30-man World Cup squad that arrived in New Zealand, and the coach is fully aware of the need for Wales to make a flying start against the Springboks despite having beaten them just once in Test history.
"The last three times we've played them there has been very little in the scores We've outscored them seven tries to six in the last three matches," added Gatland.
"We are in pretty good shape. We can match them physically, and that's the key to the battle.
"We've been 14 or 15 points up against them, and haven't been good enough or clinical enough, and have let them back into the game.
"They (South Africa) are very good at what they do in terms of set-piece.
"They put the ball up in the air, they use the power runners, they use it effectively, and they are a strong defensive side. We pretty well know what we are going to get from South Africa.
"We know how tough this group is going to be.
"If you come out of this group (at the top), you're in great shape for the quarter-finals and semi-finals, and you couldn't get any better preparation. But one step at a time: it's South Africa first and then we'll get our heads on and start thinking about Samoa."
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