The 40-year-old former Barcelona player and youth team coach only took the job at Brighton in June this year, following a spell in charge of Maccabi Tel Aviv.
The Seagulls have won two, drawn one and lost two of their first five league games this season to sit mid-table in the early Championship standings.
However, they clearly do not want another change of manager so soon after the departure of Gus Poyet, who was fired in the summer after an investigation by the club's internal disciplinary panel.
Osasuna are on the look-out for a new boss following the firing on Tuesday of Jose Luis Mendilibar.
The club's board made the decision to hire a new man after a 3-0 loss to Villarreal at the weekend made it three successive defeats to start the new season.