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Parker, a former Highlanders No 10 who has starred for the Sunwolves over the past two seasons, has another year on his contract with Kobe but could be on his way home to New Zealand as the Herald understands the Japanese club have signed former All Black Aaron Cruden on a two-year deal which could be extended to four years in total.
In a merry-go-round of Kiwi playmakers which could have wide repercussions for Super Rugby in particular, Cruden will move from French club Montpellier, where he has endured a difficult season of injury and inconsistent form, to Kobe in July. All Blacks lock Brodie Retallick will also play for the club next year during his sabbatical.
Either way, Parker won't play for the Sunwolves next year, their last in the competition, because the Japanese top league has been pushed back due to this year's World Cup and will start in January, meaning it clashes with Super Rugby.
Kobe already have the services of Dan Carter – probably only for another season before he retires (providing he recovers sufficiently from his neck injury) – and so it is possible Parker, 28, could be released from his contract.
The Herald, who revealed last week that the Blues are making a big play for Barrett, understands the franchise are also interested in Parker, an excellent goalkicker and backline organiser who has taken his game to a new level in Japan.
If he did sign, Parker has the potential to play a big part at the Blues next season even if Barrett decides to shift from the Hurricanes because it is widely assumed the two-time World Rugby player of the year will take a sabbatical from Super Rugby in 2020. Barrett is refusing to announce his plans, saying he will reveal them after the season.
In an interview with Stuff in April, Parker said his preference was to return to New Zealand. "I would love to [come home]. But I just don't know if it will all work out," he said.
The Highlanders won't have room for him because the promising Josh Ioane is locked in until the end of next year at least and the franchise will be working to keep him long term. They also have Bryn Gatland and are about to welcome Mitch Hunt from the Crusaders.
The Blues currently have three first fives: Stephen Perofeta, who didn't play a competition match this season due to a chest injury, Harry Plummer and Otere Black.
Plummer, in his first year at the franchise, shared the starting duties with Black, whose contract with the franchise came to a close after the Blues' final game against the Hurricanes in Wellington last weekend, a match they lost despite leading 24-5 at halftime.
That defeat, plus the 29-28 defeat to the Reds in Brisbane the previous week, highlighted the Blues' need for a quality, experienced, No 10.
Perofeta, 22, would have been Leon MacDonald's first pick this season but his injuries over the last two years have been big setbacks.
Plummer, 21, still has plenty of developing to do, particularly as far as his kicking game is concerned, but his bravery is not in question and he could find himself a place further out in second-five next year.
Parker is uncapped but has poise and he could play a mentoring role, too. The Blues dearly need leadership, particularly in their backline given the likely departures of Sonny Bill Williams and Ma'a Nonu.
Blues board chairman Don Mackinnon recently told Newshub: "We need leaders, no doubt about that. I'm unashamedly going to encourage the organisation to look for talent outside of the region."
Parker also has a fan in former All Blacks coach and current Blues board member John Hart, who suggested him as a possible bolter in the World Cup squad following Damian McKenzie's season-ending knee injury.
"He is experienced and one of the best goalkickers around, and brave," Hart told Radio Sport in April. "He is a bit more experienced, and you need experience in the World Cup."