Barca's star forward has 249 goals in Spain's top flight to his name, after scoring six in seven appearances this term, leaving him just two behind Athletic Bilbao legend Telmo Zarra's record total of 251.
A hat-trick would see Messi rewrite history and LFP president Javier Tebas has called for the game Messi breaks the record in to be stopped in order to mark the event suitably - though that has courted controversy with El Clasico on the horizon next week.
Barca sporting director Andoni Zubizarreta has dampened talk of such a commemoration, claiming it "smacks more of American football or basketball, which are more like spectacles and have more stoppages".
Whether Messi scores or not against Eibar, Barca will be looking to continue their excellent Liga start under Luis Enrique - the Catalans have won six of their first seven games and are yet to concede a goal domestically.
Eibar are unlikely to be daunted by that, however, following their hugely impressive introduction to top-flight football.
They have already travelled to champions Atletico Madrid and were perhaps unfortunate to go down 2-1 in a game that saw them create plenty of chances, while a 0-0 draw at Athletic Bilbao represented another creditable result on the road.
Real Madrid found form with six straight wins in all competitions before the international break, Cristiano Ronaldo scoring a sensational 13 goals in the process, but an old issue has reared its head before their trip to Levante.
Iker Casillas has seen his spot in goal come under increasing scrutiny and the 33-year-old was dropped by Spain following a high-profile error in last Thursday's shock defeat to Slovakia.
The Real and Spain skipper returned to regular Liga action this term after a season out in the cold, but Keylor Navas may well be eyeing a chance to impress this weekend at his former club.
Atletico host an Espanyol side without a win on the road since March, while early surprise package Valencia travel to rock-bottom Deportivo La Coruna.
Cordoba and, surprisingly, Athletic are level on four points with Depor in the bottom three and face respective home ties with Malaga and Celta Vigo on Saturday.
Third-placed Sevilla travel to Elche, where Fran Escriba's men have taken just one point from a possible nine this term, and Villarreal host Almeria in Sunday's other fixtures.
Real Sociedad's woeful form is belied by their 4-2 win over Real Madrid in August, and the Basque side will look for just a second success of the season at home to Getafe on Monday.
The weekend's action is kicked off by Granada hosting Rayo Vallecano.
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