The Time Person of the Year 2015 will be announced next month and the publication said the title will be bestowed on the person who "most influenced the news this year for better or worse."
Time said Modi has "encouraged foreign direct investment in India and is trying to modernise the world's largest democracy", but added that the Indian leader has also "faced controversy over what some see as right-wing extremism".
Modi was a contender for the honour last year also and while he was not chosen the Person of the Year by Time editors, he was named winner of the readers' poll, securing more than 16% of the almost five million votes cast.
On Ambani, Time said the richest person in India is the chairman of Reliance Industries "which owns everything from telecom properties to the world's largest crude oil refinery".
Also among the contenders is Pichai.
"After 11 years at Google, most recently as co-founder Larry Page's right hand, Pichai assumed the tech giant's top job," Time said.
In a separate "Face-off" poll, Modi has been pitted against Jinping, while Ambani has been pitted against Nigerian President Muhammudu Buhari.
Time asked its readers to vote for the individual who they think should get the title of Person of the Year and the winner of the reader's choice poll will be announced next month before Time's editors choose the individual from the 58 candidates as the honouree.
Modi has so far got 1.3% of the votes, the same as Pichai and Russian President Vladimir Putin.
Ambani has garnered a mere 0.2% of the votes cast.
The other candidates in the fray for the Person of the Year title include US President Barack Obama, French President Francois Hollande, Chinese President Xi Jinping, ISIS leader Abu Bakr al-Baghdadi, Democratic Presidential front runner Hillary Clinton, the refugees fleeing conflicts in Syria, Afghanistan and East and West Africa, Pakistani Nobel Peace Prize laureate Malala Yousafzai, Tesla head Elon Musk, Apple CEO Tim Cook and last year's winner Pope Francis.
From Mahatma Gandhi, Adolf Hitler, Elizabeth II to The Computer, Whistleblowers, The American Soldier and The Protester, Time has named a Person of the Year for the past nine decades.
Time said 2015 is filled with newsmakers who have defined the year.
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