Saleem began his career with
Al-Ramadi, and on 16 August 2019, he moved to
Al-Karkh, where he performed exceptionally well and contributed to the
Iraq FA Cup for the first time in the club's history win in the
2021–22 season. He also performed well the following year in the same tournament, saving three
penalty kicks in the quarter-finals against
Al-Talaba in a match that his team won on penalties and helping them qualify for the semi-finals. On 12 August 2023, he moved to play with
Al-Minaa and signed a two-season contract. However, he was unable to play with the team, due to Al-Minaa's ban by
FIFA from contracting players, Saleem moved on loan to
Amanat Baghdad in the winter transfer period. On 13 August 2024, after the ban period ended, Al-Minaa announced the goalkeeper's return from loan, and his contract was renewed for an additional season. He performed well with the team, and in the 14th round he was the fifth best goalkeeper in the league, having obtained 6
clean sheets and conceded only 10 goals. This prompted the club to renew his contract for an additional season on 20 August 2025. On 5 October 2025, he saved a
penalty kick in an away match against
Al-Quwa Al-Jawiya, taken by
Saad Abdul-Amir. ==Honours==