The Maroon 5 singer had mentored Christina Grimmie when she finished third on the American version of The Voice two years ago.
His spokeswoman, Carleen Donovan, confirmed that Levine made the offer.
When he heard of her death, Levine tweeted that he and his wife Behati were "devastated".
"Our hearts go out to her family," he wrote.
The 22-year-old was shot while she signed autographs after a concert in the city on Friday night. She died in hospital.
Police say she apparently had no personal connection to the man who shot her, 26-year-old Kevin James Loibl.
There is still no confirmed motive for the attack, but police chief John Mina said Loibl may have been a deranged fan.
After a struggle with the singer's brother, Loibl shot himself dead.
Family, friends and fans have staged a candlelight vigil in her New Jersey hometown.
Hundreds paid tribute to Grimmie in Evesham Township at the town's Memorial Complex.
She lived in the small community about 20 miles from Philadelphia, before moving to Los Angeles in 2012.
"She loved this town," her brother Marcus Grimmie told the crowd.
"She loved this state, she loved singing, she loved the Lord and she loved me."
Before appearing on The Voice, Grimmie was a star on YouTube, singing covers of other people's songs.
Her manager, Brian Teefey, has created a GoFundMe page "to assist her family in their time of need".
Teefey is also actress and singer Selena Gomez's stepfather, and both he and Gomez were very close to Grimmie.