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Newshub reports the All Blacks star is keen to make his long-awaited debut for the Blues in round 11 against the Hurricanes – his former team - at Eden Park.
The game is a week earlier than the franchise had initially planned for, with Barrett previously reported to be in camp from April 13.
Barrett is on sabbatical from the game. His last match was in the All Blacks' bronze medal playoff against Wales at the Rugby World Cup.
The 28-year-old has reportedly expressed frustration about being sidelined and is eager to play.
The decision, however, remains in the hands of the Blues, with Barrett still required to meet "return to play" protocols.
This month coaches such as the Chiefs' Warren Gatland and Highlanders' Tony Brown called for changes to New Zealand Rugby's policy of protecting their All Blacks at the expense of their Super Rugby teams.
While on break, Barrett has been in and out of Blues headquarters and was spotted on the Blues' training field before their loss to the Chiefs.
Blues assistant coach Tom Coventry said at the time that Barrett looked in good form.
"He's in great nick. He's a true professional who knows how to keep himself in shape when he's away from the game," Coventry said.
"He's going to be short of a few games of footy but we've got a plan around how we get him ready to play. It won't be too long before he's back with us."