Acuna is currently on loan with Segunda Liga side Girona, who he has helped to the promotion play-off final against Almeria.
The 24-year-old has spent the last two seasons on loan with Girona, and this season he has caught the eye of a number of clubs with his 18-goal return.
Middlesbrough are one of the clubs known to have been watching the South American closely, whilst Crystal Palace and Nottingham Forest, as well as an unnamed Ligue 1 side are also believed to be keen.
The player himself is ready to play in the two-legged final against Almeria this week, with the first leg on Wednesday and the second on Saturday, but he has admitted that there is interest from England.
"There are several team who are following me," he told Paraguayan TV show 3DFutgol.
"They are not just in Spain, I have offers from England too and I am very happy with everything that is happening.
"God willing in a week or two, we'll know where I will sign."
Real Madrid sources have told Sky Sports that no decision has been made about the future of Acuna.
"Nothing is decided on the future of Javi Acuna, until the end of the season, Girona does have an option on him," the source confirmed.
"But we also are managing offers from some foreign clubs, which the agent of Acuna is looking at and keeping us informed."