Davies (Scarlets) has been carrying a groin problem since being named in the 35-man training squad for the series, but is now expected to be available for selection against the All Blacks if required.
Fellow Scarlet Matthew Rees is also expected to come through training this week after resting, due to a calf problem, last weekend.
Ospreys hooker Richard Hibbard, who left the field against Samoa last Friday night with a shoulder injury is unlikely to take any further part in the series.
Hibbard sustained an injury to the AC joint of his shoulder following a collision early in the game and a final prognosis will be made available following his acute management and further medical discussion.
Ospreys fly-half Dan Biggar suffered a similar injury and was also replaced during the game on Friday, but his problem is considered to be less severe and it is hoped that intense treatment and management may allow him to contribute to the remainder of the series.
Finally, Ospreys lock Ian Evans took a knock to his knee, also during the clash with the South Sea Islanders, and his injury will be managed during the early part of the training week in order to give him every possible chance of being available this Saturday.
Blues lock Lou Reed and Scarlets hooker Kirby Myhill have been brought in to add to numbers in training – they join fellow Scarlet Samson Lee and Ospreys lock Lloyd Peers who have already been asked to train with the Wales squad.
No new players have yet been fully called up to the squad.
