His body was found at around 3:30 p.m. Tuesday inside his luxury seventh-floor apartment on the Lower East Side of Manhattan.
The killer was said to have abandoned the scene and escaped midway into the operation when Saleh's sister showed up unexpectedly.
Detectives believe that the motive for the killing stemmed from Saleh having discovered that Haspil had stolen roughly $90,000 from him, two of the officials said.
It was also reported that Saleh did not report the alleged theft to authorities, but brokered a repayment plan with him.
Saleh earlier this week died of multiple stab wounds to the neck and torso, the New York City medical examiner said.
Security camera video showed Mr Saleh in the apartment building's elevator with a man in a dark suit, mask and gloves, the media reports said.
A concerned cousin entered the apartment Tuesday to find Saleh had been decapitated and all four of his limbs severed and stuffed into plastic bags, according to sources.
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The killer used his employer's credit card to pay for a vehicle to a home depot, on West 23rd Street in Manhattan, to buy cleaning supplies to sanitise the crime scene, the official said.
All of the apartments in the building have private elevator access.
"Fahim is more than what you are reading", his family said in a statement. More recently, he was the CEO of Gokada, a motorcycle ride-sharing and delivery company based in Nigeria, which has faced financial setbacks and recently laid off most of its staff.
"His brilliant and innovative mind took everyone who was a part of his world on a journey and he made sure never to leave anyone behind".
Speaking to reporters about the arrest, Harrison would not say when police believe Saleh was killed, nor would he discuss other details about the case or take questions.
Mr Saleh, who was born in Saudi Arabia to Bangladeshi immigrant parents, was described as a nice and loving person who loved gadgets and video games.
Mr Saleh, who grew up in NY after moving from Saudi, founded a ride company called Pathao in 2015 and in 2018 the Gokada motorbike hailing app.