According to the Daily Star, the pair shared a private jet to the Tsaritsino Palace in Moscow, where they attended Natalia Vodianova’s Naked Heart Foundation Love Ball.
A source commented: "Natalia had a feeling they would hit it off. So she made sure they were given seats together on the jet."
The pair reportedly shared a limo back to the Ritz Carlton Hotel, and spent the night together in Borrell's room.
Imbruglia was spotted holding hands and ice skating with the rocker the day after in Red Square.
"They looked like ethereal, floating swans on the ice," added the source.
Borrell was romantically linked with Harry Potter star Emma Watson earlier this month.
Aussie singer Imbruglia split with Silverchair frontman Daniel Johns in January after five years of marriage.