Liverpool rejected Southampton's request for a permanent option to be included in their loan signing of Takumi Minamino.
The Liverpool Echo reports the Saints made their move late in the day on Monday night and had to submit a deal sheet to the Premier League in order to complete the switch.
The transfer was confirmed after 1am on Tuesday.
Liverpool will receive a loan fee of £500,000 for Minamino, which covers the sum they paid Preston to land Ben Davies.
Southampton had also pushed to make the move a permanent one at the end of the season.
Liverpool, though, rejected that proposal with manager Jurgen Klopp insistent that the versatile frontman has a long-term future at Anfield.