Career
Red Star Belgrade
Grujić is a product of the Red Star youth academy, where he went through the youth program, passed all categories and was the captain of his generation. He made his professional debut for Red Star Belgrade on 26 May 2013, in a Serbian SuperLiga match versus Vojvodina. Up to the 2015 season, he played simultaneously with Red Star and lower-tier FK Kolubara on dual registration.
On May 10, 2015, Serbian newspaper Blic reported that they had insider information that Hamburger SV intended to bid €1.5 million for Grujić.
A week later on May 17, 2015, Grujić signed a three-year contract with Red Star to last until 2018. Grujić scored his first senior goal against Novi Pazar.
He also assisted Aleksandar Katai for the second goal in the last minute of the game. His next goal came in the next round against Spartak, an equalizer which lead to Red Star winning the match 3–2, and to a ninth consecutive victory.
Grujić scored from long range against Rad in the King Petar I Stadium, his third consecutive goal.
From the fall of 2015, Grujić was a part of an unprecedented run of Red Star victories, as the club set a new record by the number of consecutive victories (19), ending first half of the season without defeat, with 25 points advantage over the runner-up team Throughout the autumn, Grujić was scouted by a number of established European teams, including Liverpool, Internazionale, Juventus, Chelsea, and Milan. Jurgen Klopp"s assistant from Borussia Dortmund, Željko Buvač flew to Belgrade to speak with Marko.
Liverpool
On January 6, 2016, it was confirmed that Grujić completed his move to Premier League side Liverpool, signing a five-year deal for reported fee of £5.1 million.
Despite being Jürgen Klopp’s first signing, he was immediately loaned back to Red Star, until the end of the season for a fee of £740,000. Upon joining, Grujić hailed Klopp for convincing him to join and told the press, "I would choose Liverpool over Real Madrid and Barcelona".