It’s believed the ambitious expansion club offered the 31-year-old a three-year deal worth in excess of $750,000-a-season.
But, it’s understood, the Sky Blues are prepared to trump even those figures - which equate to $2.25 million over three years - with a marquee-style offer Krishna will find impossible to ignore.
Whilst several other clubs remain keen to capture Krishna, Sydney appear set to outbid all comers.
Melbourne Victory’s off-contract Kiwi attacker Kosta Barbarouses is also on a short-list of targets, with the Sky Blues gearing up to fill the slots created by the anticipated departures of loan signings Siem de Jong and Reza Ghoochannejhad.
However, the Sydney hierarchy believe it’s more likely Barbarouses will re-sign with Victory, or possibly switch to Asia.
At 31, off-contract Wellington attacker Krishna has enjoyed the most productive period of his career with 19 goals in 27 games taking him to previously unprecedented heights.
His best previous tally in six years with the Phoenix was 12 goals in 2016-2017. On four other occasions he failed to break double figures.
While he has surpassed Paul Ifill as Phoenix’s all-time leading scorer with 51, it’s taken Krishna 132 games to reach that tally.
However, Sydney are convinced he can sustain his late-career goal burst under coach Steve Corica’s influence.
Phoenix, who will be coached by current Sydney FC assistant Ufuk Talay next season, have made what they believe is a temping extension offer to Krishna, and are hoping his affection for the club keeps the suitors at bay.
He penned a heartfelt note on his Facebook page thanking the club’s fans for their backing during the season after their 3-1 elimination semi loss against Melbourne Victory.
It offered a slither of hope that he might stay, reading in part: “it’s not the end ... for now we all take a short break before we pick up again.”
With A-League business to take care of first - foremost Sunday’s semi-final against Melbourne Victory, Sydney’s hierarchy are unlikely to lock in any new signings until their season is over.
Sydney FC declined to comment when contacted by The World Game.