The report claims Perez is wanted to provide the Premier League champions with competition for Jamie Vardy, and there are obvious similarities between the two players.
Perez has stood out with his pace and clinical finishing this season, coming from nowhere to score 17 La Liga goals and a further two in Europa League qualifying.
Previously, the 27-year-old had failed to make the grade in Spain, and spent time in Ukrainian and Greek football - the latter while Leicester boss Claudio Ranieri was managing the national team.
According to the Guardian, Ranieri is confident of landing another La Liga player, in the shape of Sporting Gijon centre-back Luis Hernandez, who is available on a free transfer.
Perez, though, could be more difficult to snare. The left-footer has three years left on his contract, not to mention a strong affinity with Depor - his hometown team.
But a move to Leicester, who will make their Champions League debut in September, certainly has its merits and the Foxes are apparently ready to exceed the £9 million they paid for Andrej Kramaric to land him.