Watford and Nottingham Forest are both keen on the right-back and Deportivo could be forced to sell due to financial problems.
Laure has stated he would love to come to England and he has the potential to be a success in British football.
The player's UK representative, Jonathan Hope, said: "The interest from England for this experienced player has soared over the past week at an increasing pace.
"He is a player of the highest quality and wants to come to the UK. It is sad that Deportivo are in the financial situation they are in but that is business and players need to move on.
"Laure has been assigned to mark Lionel Messi, Cristiano Ronaldo and Andres Iniesta to name a few.
"He is a premier league player and at the age of 28 has a huge future in English football."