Jones has not played since the Six Nations defeat by England because of a heel injury, and will miss Ospreys' Pro12 match with Ulster on Saturday.
Wales travel to the world champion All Blacks for a three-Test series in June.
Asked if lock Jones would make the tour, Ospreys backs coach Gruff Rees said: "The work he's doing now would suggest it's a large possibility."
Rees added: "If you asked Alun himself he would say 'certainly', but he's probably got a few thing he has to tick off yet."
Wales, whose last victory against New Zealand came in 1953, have never won an away Test against the three-time World Cup winners.
Jones, the British and Irish second row and Ospreys captain, is on a dual contract as the Welsh Rugby Union (WRU) covers 60% of his salary.
The 30-year-old has been working with medical staff from the WRU and Ospreys as part of his rehabilitation, with Rees saying the player is making progress as Wales head coach Gatland hopes for a memorable win in his home-land of New Zealand.
"He's doing physical based work. There's a skill element to what he's doing in partnership with the governing body as well," added Rees.
"He's in good spirits. He was in the coaches' box at the weekend [against Cardiff Blues] and I enjoyed having him in that area and he's contributing off the field with some of our planning."
If he makes the tour party, Jones is set to make his 100th appearance for his country.
Has has won 98 Wales caps, in addition to five Test match appearances for the British and Irish Lions.
His absence this weekend is a blow to the Ospreys, who need to beat Ulster at the Liberty Stadium to maintain their chances of playing in the European Champions' Cup next season.
Ospreys are the only Welsh team to have played in the top-flight European competition every season since the introduction of regional rugby in 2004.
Warren Gatland has been told there's a "large possibility" Alun Wyn Jones will be fit for Wales' tour of New Zealand.