Vojvodina

Katai started playing football for his hometown club FK Vojvodina youth squad. After a six- month loan to lower league team FK Palić at the start of 2009–10 season, he was promoted to Vojvodina's first team.^[2] His debut in Serbian SuperLiga was on 14 March 2010, when he came in as substitute against FK Čukarički, and he scored his first goal just seven days later in a match against Mladi Radnik. On 28 June 2011, he left FK Vojvodina and went to Athens to join Olympiacos.^[3]

Olympiacos

On 24 June 2011, Olympiacos agreed to sign Katai on a four-year contract.^[4] At his first trainings with the club, coach Ernesto Valverde told Katai that he did not defend enough and that he needed to improve as a player.^[5] Katai did not play a single match for Olympiacos, but was instead sent on loan four times.

He was first loaned to OFI Crete, with whom he made his debut on 5 November 2011, against Panionios.^[6] The loan spell to Crete was unsuccessful, and so Olympiacos loaned him back to his hometown club FK Vojvodina. While on loan at Vojvodina, in 2012 after one game with Spartak Subotica, he fell very ill and was admitted to the hospital, where he was diagnosed with thrombocytopenia.^[5] He had to have some blood removed, and stayed in the hospital for two weeks before he was allowed to finish his recovery from home.^[5] During his recovery, he gained over 20 pounds, and he did not return to play football until the end of the year.^[5] He remained a loaned player for Vojvodina until the club president Ratko Butorović died unexpectedly on 8 June 2013, which led to a period of instability in the club during which Katai left.^[7] He subsequently was loaned to Platanias, for whom he scored a total of eight goals and six assists,^[5] until his loan there expired in the summer of 2014.

Red Star Belgrade

Alavés

On 31 August 2016, Katai signed a three-year contract with La Liga side Deportivo Alavés, for an undisclosed fee.^[14]

Chicago Fire

On 6 February 2018, Katai was loaned by Alavés to Chicago Fire of Major League Soccer. The loan was for the 2018 MLS season and included a purchase option at season's end.^[15]

On 11 July 2018, the Chicago Fire acquired Katai on a permanent basis from Alavés for an unknown amount. The deal had Katai signed through the 2019 season, with a club option for 2020. It also had him remaining a TAM player for the 2018 season, but would change to a DP in 2019.^[16]

LA Galaxy

On 31 December 2019, after leaving the Chicago Fire, Katai joined the LA Galaxy through the use of Targeted Allocation Money.^[17] Katai was expected to be an important part of the Galaxy’s attack in 2020.^[18]

Katai was released by LA Galaxy on 5 June 2020, following controversial Instagram posts by Katai's wife, Tea, in the wake of the George Floyd protests and looting across the United States.^[19][20] Katai's wife, writing in Serbian, had compared protestors to "disgusting cattle", called for violent action against them in a caption under a photo of New York Police Department officers driving an SUV into a crowd of protesters ("shoot those s***s"), and captioned an image of what appears to be a looter running off with boxes of Nike sneakers with "Black Nikes Matter".^{[21][22][23][24]}

The LA Galaxy requested the removal of his wife’s posts and issued a statement condemning "racism of any kind".^[21] Tea then took down the posts.^[21] In an Instagram post, Katai condemned his wife's posts as "unacceptable", rebuked her insensitivity, issued a personal apology, and indicated his support for the Black Lives Matter movement.^{[25][21][26][27]} Two days after the team became aware of the wife's posts, which also was two days after his post condemning her statements, and following a day of protests against Katai, the LA Galaxy released him.^[21][25]

Return to Red Star Belgrade

On 9 July 2020, Katai signed a two-year contract with Red Star Belgrade.^[28]

Club

As of match played 2 May 2024^[31]

International

As of 12 November 2020^[32]