Williams was a notable omission when the Kiwis' 24-man squad was named on Tuesday to defend the title in Europe.
Kearney says the second-rower is unavailable "due to other commitments".
"What they are, at this stage we would all like to know," he said.
"I'm sure we'll all hear about that after the next two to three weeks."
Williams, who has been tipped to return to rugby union with the Chiefs, said after helping the Sydney Roosters to the NRL premiership on Sunday that he would take a couple of weeks to decide his footballing future.
Williams told fans on Twitter that he needed some down time.
"Wishing the kiwis all the best in their title defence, having my first break since 2008. Looking forward to spending time with fam n friends," Williams posted on Tuesday.
Kearney said he had sensed for some time that Williams would not be available for the World Cup.
"We had planned that Sonny wasn't going to come away," he said.
"That was, I guess, just the general feeling that I had throughout the year."
Kearney said he had been in talks with Williams' manager, Khoder Nasser, for the past six to eight weeks.
He said Nasser had been upfront with him and had told him he didn't know himself what the player would be doing.
Kearney also spoke to Williams on Monday, but declined to reveal the contents of the conversation.
The 24-man New Zealand squad contains two uncapped players in two other Roosters - Dally M winger of the year Roger Tuivasa-Sheck and prop Sam Moa.
Apart from Williams, Kearney said other players out of selection reckoning were Newcastle back-rower Jeremy Smith and Roosters centre Shaun Kenny-Dowall.
Smith, who played in 2008 World Cup final win over Australia, is unavailable for family reasons.
Kenny-Dowall is out because of injury after playing most of the grand final with a broken jaw.
Kearney and the squad will gather in Sydney on Saturday before flying out for Britain.
The Kiwis have a warm-up fixture against the Cook Islands in Liverpool on October 21 (AEDT), before beginning their cup defence against Samoa in Warrington seven days later.
NEW ZEALAND RUGBY LEAGUE WORLD CUP SQUAD
Jesse Bromwich (Melbourne), Greg Eastwood (Canterbury), Kieran Foran (Manly, vice-captain), Alex Glenn (Brisbane), Bryson Goodwin (South Sydney), Tohu Harris (Melbourne), Joss Hoffman (Brisbane), Krisnan Inu (Canterbury), Shaun Johnson (Warriors), Sam Kasiano (Canterbury), Thomas Leuluai (Warriors), Kevin Locke (Warriors), Issac Luke (South Sydney), Simon Mannering (Warriors, captain), Ben Matulino (Warriors), Sam Moa (Sydney Roosters), Jason Nightingale (St George Illawarra), Frank-Paul Nu'uausala (Sydney Roosters), Frank Pritchard (Canterbury), Elijah Taylor (Warriors), Roger Tuivasa-Sheck (Sydney Roosters), Manu Vatuvei (Warriors), Jared Waerea-Hargreaves (Sydney Roosters), Dean Whare (Penrith).