With Ernesto Valverde still in place, Barca management have held talks with former captain Xavi about leaving Al Sadd and succeeding their head coach.
Mauricio Pochettino was one of three candidates considered at a tense board meeting in the afternoon.
Valverde is the first coach Barca have dispensed with in the middle of a campaign since Louis van Gaal was sacked in January 2003 with the team sitting 12th in the standings.
The club said it reached an agreement with Valverde to terminate his contract.
The 39-year-old Xavi, who won the World Cup with Spain in 2010, came through Barcelona's academy and played 855 senior games for the club.
Quique Setien and former Barcelona defender Gabriel Milito are the other two names on Barcelona's shortlist.
"Setien is one of the most experienced coaches in Spanish football", it added.
They return to action on Sunday against Granada and it remains to be seen who will be in the Nou Camp home dugout.
Setien has expressed his admiration on everything that Barcelona represent, focusing on their attacking style of football.
A former player of Atletico Madrid and Racing Santander, he was circled as a potential Barca coach during a particularly successful period in charge of Real Betis.
Setien had been with Betis since 2017 until deciding to take some time off at the end of last season.
Betis finished 10th and the club and coach parted ways in the summer.
And domestic success means little if, say, the team squanders a 3-0 advantage and exits Europe's premier cup competition in inglorious fashion. Barcelona is also dealing with some injury woes asas star striker Luis Suarez will be out for four months due to a knee injury.
But Champions League collapses against Roma and Liverpool have not been forgotten and poor performances in recent weeks have prompted fears of a repeat.
Barcelona's shocking collapse against Roma in 2018 was followed by a similar capitulation against Liverpool previous year.
A delegation is understood to have met with the club's record appearance holder in Doha last week, although Barcelona were reluctant to reveal the true nature of the discussions. "Both of them have been at Barça and know the club". On Monday, Barcelona decided his time was up.
Instead, he steadied the ship and galvanised the team.
Increasingly, though, Valverde's achievements faded from view and his failures began to overshadow them.