The four-time Ballon d'Or winner has not played since sustaining a hamstring injury in a 4-1 win at Real Betis on Nov. 10.
The Argentine superstar returned to training this week, scoring a hat trick in a practice match on Friday, but Sunday's match has come too soon for the 26-year-old, who is more likely to be ready for the huge game against second-placed Atletico Madrid next weekend.
However, Barcelona does welcome back Victor Valdes. The goalkeeper, who is set to leave the club at the end of the season, is available again following his recovery from a calf problem and is in line to replace Jose Manuel Pinto in between the posts.
Meanwhile, Sergio Busquets is banned after picking up his fifth booking of the season in the 5-2 win at Getafe prior to Spain's midseason break.
That victory represented Barcelona's fifth in succession across all competitions and the Catalan club has dropped only five points in La Liga this season.
In contrast, Elche has won just four league games and begins the new year two points above the relegation zone, in 14th.
Elche is missing two players - Damian Suarez and Coro - through suspension and will be a huge underdog to take anything from Camp Nou in its first top-flight season since 1989.
Fran Escriba's men have lost four of their previous five matches and boast only one victory in 10 outings - a 2-1 triumph over Valencia on November 24.
Barcelona heads into Sunday's match having won a remarkable 23 Liga games in succession on home soil, firing in 80 goals in the process.
Addressing the media on Friday, Escriba acknowledged his side faces the stiffest of challenges, but called for a positive approach.
"We have to be brave and try to find the goal because it is difficult to think that they (Barcelona) will not score," he said.