Both players are suffering from knee injuries and will miss the game in Dublin on Sunday week, while Jenkins may be sidelined for up to five weeks and also miss Wales' second game of the tournament against Scotland on February 12.
"Gethin is struggling and could be out for four to five weeks," said Warren Gatland. "Rhys will be struggling for the first game. We're assessing him day by day.
"Gethin is a huge loss for us for potentially the first two games of the tournament. He's been playing exceptionally well for the Blues in the last month.
"He's a world class player. He's got a very good rugby brain and is able to asses things on the field. He's almost like a coach on the field.
"You get a lot of information from him at half-time, what's going right or wrong, tactically where we need to change.
"Rhys was probably the find, if not the best, fly-half at the World Cup. He really does fit the type of game we want to play.
"His kicking game and vision are excellent. He stretches opposition defences as well because he's not afraid to run.
"There's a very good balance to his game. You can't underestimate the space he created for our midfield at the World Cup.
"He was one of the reasons we saw some really big performances from Jamie Roberts, Jon Davies and Scott Williams. He will be a big loss for us.
"But there's experience to come in with James Hook and we may look at Gavin Henson in that position too."
Gatland revealed Leigh Halfpenny is likely to take over the kicking duties in Priestland's absence.
Flanker Dan Lydiate is also a doubt for the trip to Lansdowne Road because of an ankle problem, but centre Jamie Roberts (knee) is expected to be fit to play.
"Dan Lydiate is touch and go. We're hoping Jamie Roberts will be OK," Gatland added.
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