The jostling between

Warner Music

(WMG) - Get Report



is getting rougher.

On Wednesday, word emerged from EMI that Warner has twice offered to buy the British recording giant, with the latest offer coming in at $4.56 billion. EMI, which has its own offer on the table for Warner, rejected the proposals.

EMI previously floated an offer to acquire Edgar Bronfman Jr.-led Warner Music for $28.50 per share, or $4.2 billion. That offer was swiftly rejected by Warner's board. In a statement Wednesday, EMI said it raised the proposal to $31 a share -- and Warner rejected it again.

Warner's shares closed at $27.23 Tuesday.

In late May, EMI said it continues to believe "an acquisition of Warner Music by EMI would be very attractive to both sets of shareholders, but we will only pursue a transaction that delivers enhanced value and earnings accretion to our shareholders."

A joint group would create the world's third largest music company after Sony/BMG and Universal.