However, should Alphabet proceed, it could result in Google investing somewhere around $1 billion in Lyft, something that itself was recently tipped as eyeing a possible expansion of its services into Canada.
The two companies have already forged strong ties.
Such an injection of support from one of Silicon Valley's largest companies would certainly be a boost as it aims to grab more of Uber's market share.
Alphabet has been exploring closer ties with Lyft ever since it fell out with Uber.
However, Alphabet's self-driving vehicle unit Waymo is now suing Uber for alleged use of stolen Waymo trade secrets to develop Uber's self-driving technology, thus complicating the relationship between Alphabet and Uber. Lyft's most recent financing, a $600 million round that closed in April, was led by KKR.
Lyft has already risen more than $2bn worth of funding working with investment backers including the partnership with Waymo to test self-driving cars as well as General Motors, Rakuten, and Floodgate. And Alphabet, Google's parent company, is about to haunt Uber.
Lyft is in competition with Uber among ride-hailing services in the USA, while Waymo is competing fiercely with Uber in the creation of technology for autonomous cars.
Neither Alphabet nor Lyft would comment on the report.
Uber is now in the process of trying to secure more funding, with Lyft set to expand into Canada - which would be its first global expansion. Uber sales have slipped throughout the year from lawsuits, former CEO Travis Kalanick stepping down, probing into competitors, and evading government regulations and officials.