Textiles millionaire Rajesh Juneja told BBC Hindi he would place the suit next to a statue of Mr Modi and talk to it every day to gain inspiration.
Mr Modi wore the suit, decorated with pinstripes made from his name, at a meeting with US President Barack Obama.
He was criticised after reports said it cost nearly 1m rupees to make.
The proceeds will be used to clean the heavily polluted river Ganges.
The clean-up is a pet project of the prime minister, and his government has set a target to complete the task within three years.
The auction is due to close at 17:00 (11:30 GMT) on Friday.
Within hours of the sale opening, textiles millionaire Rajesh Juneja had bid 12m rupees.
"I am big fan of Narendra Modi," the 57-year-old told BBC Hindi.
"I like his style of functioning and after buying this suit I will keep it my office along with his statue and talk to it everyday as it will inspire me to achieve more."
His offer overtook several other businessmen in Mr Modi's home state of Gujarat who had already bid huge sums for the suit.
But experts say the suit is likely to sell for much more by the time the auction ends.
It is being sold along with more than 450 presents that Mr Modi has received since taking over as the prime minister.
Mr Modi was photographed in the suit at meetings with Mr Obama during the US president's three-day state visit to India in January.
Senior Congress party politician Jairam Ramesh had called Mr Modi a "megalomaniac".
Mr Modi is not the first high-profile figure to opt for the pattern - in March 2011 former Egyptian President Hosni Mubarak was photographed in a similar suit.
An Indian businessman has bid more than 12m rupees ($194,000; Â£125,000) for a suit worn by PM Narendra Modi at the first day of a three-day auction.