The winger had attracted the interest of Arsenal and Aston Villa over a move, but French giants PSG look set to win the race.
It was revealed earlier in the week that Asensio would depart Madrid at the end of the season after negotiations over a new deal broke down.
After winning a multitude of honours over the course of nearly a decade at the Santiago Bernabeu, he will leave as a free agent.
Appearances in the Madrid starting XI have been limited this season but his 12 goals and eight assists prove he has quality when he plays.
Asensio was likely to be a sought-after player in the transfer window, but it appears his next club has already been decided.
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The Athletic report that he will sign for PSG, with a long-term agreement in place between the player and club.
Asensio will earn around £8.5million-a-year at the French giants with his salary and bonuses and the transfer will be completed after the weekend.
The visit of Athletic Bilbao on Sunday will be his final chance to play in a Madrid shirt as he prepares to move to pastures new.
Premier League football could very well have been an option for him next season, but Arsenal and Villa appear to have lost out on a target.
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Interest in the 27-year-old has been shown in the past by a Gunners side who will be keen to compete for the Premier League title again next season.
talkSPORT understands that Villa have been in talks to sign him as Unai Emery's side look to backup their qualification for European football in the transfer market.
However, Paris looks set to be Asensio's next destination as he switches one European capital for another.
He will leave Madrid with three La Liga and three Champions League titles to his name as well as other domestic, continental and international successes.