The Spain international - who is currently representing his country at the Tokyo 2020 Olympics - has seen his Bernabeu future called into question as Real Madrid prepare to hand more opportunities to Vinicius Junior, Rodrygo Goes and Takefusa Kubo.
Asensio's existing Real Madrid deal expires in 2023 and it seems unlikely that he will pen an extension, meaning that the capital giants would be under pressure to offload him this year or in 2022.
According to Spanish outlet Fichajes, the 25-year-old has garnered significant interest from the Premier League, with Everton, Leeds United and Leicester City all making contact with Real Madrid over a possible move.
Asensio has assisted one goal in four appearances so far for Spain's Olympic squad, who face Japan on Tuesday lunchtime for a spot in the gold medal match.
The former Mallorca youngster has won two Champions Leagues and two La Liga titles at the Bernabeu, scoring 37 goals and setting up 22 more in 193 appearances. body check tags ::