According to trade magazine Architects' Journal, which has been running a series of exposes on the matter, Boris Johnson and Garden Bridge designer Thomas Heatherwick travelled to the tech giant's San Fransisco base in February 2013.
Days later Hetherwick then took part in Transport for London's bridge contest, which he went on to win.
Len Duvall, chair of the London Assembly's oversight committee - which has been investigating the procurement of the bridge for several months - told the AJ: ‘If…the Mayor has been caught travelling to America on taxpayers' money to promote Thomas Heatherwick’s Garden Bridge before the procurement process had concluded it would show the utter contempt Boris has for the rules which are specifically in place to prevent undue influence.
"This debacle is increasingly looking like a scandal and we now need full disclosure."
He added: ‘Boris Johnson needs to start being entirely upfront about his role in the procurement process. We’ll be pushing him to come clean about exactly why he misled the Assembly, willingly or not."
Caroline Pidgeon, leader of the Lib Dems in the Assembly, who is running as her party's mayoral candidate, branded it a "cover up".
She added: "It is staggering that the Mayor of London, who is also the chair of TfL, considered it acceptable to fly at taxpayers’ expense all the way across to San Francisco to seemingly drum up support for Thomas Heatherwick’s proposal for a Garden Bridge when TfL had not even published their invitation to tender."
Johnson has previously refused to name who he met, claiming this would prejudice ongoing conversations with the potential sponsor. He also failed to report the trip in his monthly report to the London Assembly and had listed it as a ‘private trip’ in his diary when released under FOI.
However, the £10,000 bill was picked up by the taxpayer, the AJ claims.
A spokesperson for the Mayor of London told City A.M.: "The Mayor met with Apple in 2013 to discuss a number of investment opportunities in London. Thomas Heatherwick was also in California to meet a separate commitment with Apple. Given that he had already expressed interest in creating a Garden Bridge, the Mayor invited him to join the meeting and outline his ideas.
"That meeting had no bearing on the procurement process led by Transport for London for the design of the Garden Bridge, which was open, fair and transparent."
A source close to Apple told the AJ: "Apple has no involvement in this bridge project and is not considering getting involved."