Asensio joined PSG as a free agent in July 2023 after over eight years with Real Madrid where he won three Champions Leagues and three LaLiga titles, and in his first season with the French club won the domestic double.
The 29-year-old, who has made 38 appearances for Spain, has scored two goals this season in 16 games for PSG, but Asensio has played just 18 minutes in the last eight league games for Luis Enrique's side.
Villa, who are eighth in the Premier League standings and qualified for the last 16 of the Champions League, host Tottenham Hotspur in the fourth round of the FA Cup on Sunday.
Marcus Rashford arrived at Villa on loan from Manchester United on Sunday.
