A week ago Rodgers was joint favourite with one bookmaker to become the first Premier League manager to get the sack this season, but back-to-back wins have brought some of the feel-good factor back to Anfield.
Ahead of Saturday's visit of Sunderland and a crucial run of matches including a make-or-break Champions League clash with Basel and Premier League tussles with Manchester United and Arsenal, Rodgers heralded a "real and exciting period of games".
After three straight league defeats at the start of November, his mood has been buoyed by last weekend's 1-0 victory over Stoke City and a 3-1 success at Leicester City, while Ayre's comments are only likely to bring further cheer.
"There was no speculation on our part," the CEO told Sky Sports.
"Lose a few games and the whole world turns but certainly not within this football club and our fan base. The manager has great support, we work as one team, we are all together, nobody's running scared and we are very pleased."
At the heart of Liverpool's recent revival has been Lucas Leiva, whose return to the side has provided some previously absent steel to a midfield that was too often exposed in the early part of the campaign.
In what is likely to be music to the ears of many fans, Rodgers confirmed the club had received no offers for the Brazilian who has long been linked with a move away having struggled to oust captain Steven Gerrard from the midfield anchor role.
"He was always an important member of the squad. He's in a good moment and long may it continue," Rodgers told reporters on Thursday.
On the injury front, Rodgers confirmed that striker Mario Balotelli was still unavailable, while Daniel Sturridge, who has not played since suffering a thigh injury with England in September "has gone away to get some work in, with some of our staff, doing specific work".
Off the pitch, the club confirmed their stadium expansion, which will add 8,500 seats to take the capacity to around 54,000, with construction set to begin on Monday.
"Today is an important milestone in the history of Liverpool Football Club," Ayre said on the club website.
"Since we embarked upon this journey we have always said that we need certainty; we now have that certainty."
(Reporting by Toby Davis; editing by Justin Palmer)
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