The club are currently being coached by former player Alan Shearer who agreed to return as manager for the last eight matches of the season as Newcastle battle to avoid relegation from the Premier League.
Kinnear has been recovering from triple heart bypass surgery in February.
"Joe had his tests on Monday and the doctors were pleased with him," Llambias told The Northern Echo newspaper.
"He's lost two stone in weight and has passed all his tests with flying colours. He's on the mend - in two months' time he should be fully fit."
Llambias said there was no possibility that Kinnear would work again this season.
Kinnear replaced Kevin Keegan as manager in September when the club were one off the bottom of the table. He lifted them to 13th place before being taken ill before the away match against West Bromwich Albion on February 7 - their last league win.
Under caretaker coach Chris Hughton they slipped back into the relegation zone, and remain there following Shearer's first match in charge last weekend - a 2-0 home defeat by Chelsea.
Shearer has said he will return to his job as a pundit on BBC television after the end of the season.
NEWCASTLE FANS! Check FourFourTwo.com’s ever-expandinginterviews archivefor more stuff to read:
Web Exclusives Les Ferdinand
Q&A Joey Barton
One on One Michael Owen, Kevin Keegan, Les Ferdinand, Faustino Asprilla
Boy's A Bit Special Steven Taylor, Danny Guthrie
Ask A Silly Question John Barnes
Perfect XI Ruud Gullit
What Happened Next? Tony Cunningham
My Secret Vice Nolberto Solano, Sam Allardyce
Plus! Rate Newcastle players (and others) on Talentspotter
