The former couple are both scheduled to perform at the February 20 event, causing a headache for organisers since they split last month.
The initial plan had been for Styles and his One Direction bandmates to rehearse on Tuesday (February 19) alongside Justin Timberlake, Muse and Swift.
"It was a bit of an oversight to say the least. The original plans were drawn up a while back when Harry and Taylor bumping into each other wouldn't have been an issue," a source told The Sun.
"But they've had to have a bit of a rethink now. Mumford & Sons were meant to be rehearsing on the Monday with Robbie Williams, Emeli Sandé and Ben Howard - but they were happy to switch.
"It could have caused a bit of a headache if the Mumfords kicked off - but fortunately they played ball."
Styles and Swift managed to avoid each other when they both attended the NRJ awards in France last month.
Watch Taylor Swift's video for 'We Are Never Ever Getting Back Together' below: