The artists will record a cover of REM’s ballad Everybody Hurts.
The Sun newspaper, which has teamed up with Cowell, said Robbie Williams, Coldplay, Take That and Sir Paul McCartney have also been approached.
Meanwhile, Madonna and Beyonce will take part in a global telethon to raise cash for the earthquake-hit country.
Performances for the Hope for Haiti event will be screened on every major TV network in the US and streamed on websites around the world.
Other acts taking part in the telethon include U2′s Bono and The Edge, Jay-Z and Rihanna, who will all be performing together in London.
Wyclef Jean, who is a Haitian-American, Bruce Springsteen, Jennifer Hudson, Mary J Blige, Shakira and Sting will perform in New York.
Hollywood actor George Clooney has organised the event.
Speaking to MTV, he said: “It’s a big world out there, and we all have a lot of responsibility to look out for people who can’t look out for themselves.
“So what we can do is first and foremost, raise money. If I thought we could all pick up shovels and go in there and help without being in the way, I think a lot of people would do that.”
The proceeds from the single, which is being organised by Cowell, will be split between the Disasters Emergency Committee (DEC) and the Sun’s Helping Haiti campaign.
The Government has already agreed to waiver VAT on the record and REM, who own the rights to the song, have also waived royalties on the charity track.
“We are all working hard to make this single a success and to raise lots of money for Helping Haiti,” Cowell said.
“We have a short time to do this and the people in Haiti need as much help as we can possibly give them as soon as possible.
“I’d like to make this record with as many different types of singer as we can and I hope everyone in the industry comes together to get involved. The response has been fantastic.”
Will Young, X Factor winner Joe McElderry and hip-hop trio N-Dubz are also said to have expressed an interest in singing.
Prime Minister Gordon Brown, who apparently requested Cowell organise the charity track, said he thought the single would make a big difference.
“The agony and anguish for the people that we are seeing on our television screens is something that British people want to respond to.
“Simon Cowell can make a huge amount of money to help the people of Haiti.”
Artists have also agreed to take part in a special eBay auction, which has been set up by Glastonbury organiser Emily Eavis.
Coldplay, Damon Albarn, the Arctic Monkeys, the Chemical Brothers, The Kooks, The Pet Shop Boys, Klaxons and Pearl Jam have all donated various pieces of rock memorabilia for the sale.
It goes live from 0900 GMT on Friday and will run for 10 days.
Coldplay’s Chris Martin added: “I visited Haiti with Oxfam a few years ago. It’s a country of extreme poverty and brutal living conditions. Most people in Port-au-Prince live in tin shacks.
“The earthquake that has struck Haiti will have turned the city into an unimaginable hell.”
An estimated 1.5 million people were left homeless by the 7.0-magnitude quake, which is believed to killed as many as 200,000.
At least 75,000 bodies have so far been buried in mass graves, the government has said. Many more remain uncollected in the streets.
