Messi appeared to have been injured after a tackle by Manu Trigueros.
Atletico Madrid dropped three crucial points after losing to Athletic Club Bilbao on Sunday.
There has been no progress in the club captain's contract renewal.
The defending champions dropped two crucial points against Real Betis.
The Belgian will be hoping to recover fully and avoid another injury before the end of the season.
The Barcelona captain said last year that he is open to playing in the MLS.
Both clubs won their latest matches to keep the title race extremely tight.
Real Madrid temporarily leads La Liga after the victory against Cadiz on Wednesday.
Gerard Pique says the Super League "destroys the system" of football.
The results in the coming weeks will likely determine the future of both Messi and Koeman with the club.
Zidane refused to weigh in on the controversial league in his press conference ahead of the match against Cadiz.
Los Blancos dropped two crucial points in the goalless draw against Getafe on Sunday.
Sky Sports reported that Liverpool, Manchester United, Arsenal and Chelsea were among six Premier League teams set to be part of the plans.
The Copa del Rey victory may help Messi decide to stay at the Cam Nou.
Vinicius, Valverde, Rodrygo and Odegaard are not going anywhere.
Messi wore the boots when he broke Pele's record for most number of goals for a single club.
Los Blancos is at risk of losing more starters to injury if Zidane does not find a way to rest them.
Atletico has seen their 10-point lead disappear in under three months.
With matches being played behind closed doors, football clubs are missing out on massive revenue.
Real Madrid defeated Barcelona 2-1 on Saturday.
Los Blancos claim the top spot in the La Liga table as they wait for Atletico's result.
Real Madrid will host El Clasico on Saturday at their temporary home ground at Valdebebas.