Leganes are nervously waiting on a reply from Mauricio Pellegrino over the vacant managerial role.
The Madrid based club saw Asier Garitano leave for Real Sociedad earlier this week and they have attempted to move quickly to replace the talented coach.
46-year-old Pellegrino is currently without a job after a dismal time in England with Southampton, following spells with Valencia, Estudiantes, Independiente and Alaves.
The Argentine is understood to be in Spain at present and is said to be weighing up the job offer submitted by the Buturque outfit.
A decision is said to be set for the next few days, leaving Leganes nervously waiting.
Should Pellegrino not decide to take over – then the likes of Jagoba Arrasate, formerly of Real Sociedad, has been linked.
Arrasate, is currently in charge of Numancia, who are in the play-offs for a place in La Liga next season and success would see a move to Leganes seem unlikely.
Leganes had a superb start to the season under Garitano, but results towards the back end of the campaign saw them eventually finish just above the relegation zone.
Despite that dip in form, Garitano was instantly wanted by a number of clubs and in particular – Real Sociedad, where he will not build on their good end to the campaign.