Northern Districts chief executive David Cooper confirmed talks were continuing with Gayle, who has been a spectacular success for the Thunder, hitting an unbeaten century off 54 balls against Adelaide at the Sydney Cricket Ground before Christmas.
That included 11 sixes, the most in Australian domestic Twenty20 history.
He has also recorded two half centuries, including a 75 against the Melbourne Renegades.
It is understood the pitch would be around playing alongside fellow international cricketers Daniel Vettori and Brendon McCullum and having a bit of fun, rather than the promise of any significant financial reward.
Gayle is due to remain in Sydney for the rest of the week following last night's match for the Thunder, which was effectively a dead rubber given the team - seventh of eight going into their last match - has no chance of making the play-offs.
Cooper said Gayle was not a confirmed starter and negotiations were continuing. But he added that Gayle wasn't the only player on his wishlist. "There's probably him and others that would be of value in coming across to help out with our gate receipts and things.
"We are probably sitting and hoping on a whole lot of things but there's nothing I can confirm.''
Cooper said he couldn't comment on which other players he was targeting. "We're in confidential talks with some people,'' he said.
The Knights' previous international signings have been made in the hope that they would help with entry into the lucrative Champions League, but this signing would be solely about trying to fill the coffers.
The rise of the Twenty20 game means the sight of international players jetting in for one or two domestic games has become the norm.
Vettori and McCullum have both played two matches for the Brisbane Heat in this season's Big Bash. Vettori hit 40 against the Melbourne Stars last Thursday night and McCullum's highlight was a 36, also against the Stars, on December 20.
