His mother, Syeda Fatina, was a descendant of the Dewan family of Haibatnagar, tracing her lineage from her father's side.

[12] In 1966, Salman and his older brother, Sohail Fasihur Rahman, began managing a family-owned jute factory.

[15][6] The company is listed in Aim of London Stock Exchange[16] and also accredited by many foreign regulatory authorities including the US FDA for its export operations.

[27][28] Salman was appointed as the Private Industry and Investment Advisor to Prime Minister Sheikh Hasina on 15 January 2019.

[30] Rahman was tasked by the prime minister to improve Bangladesh's standing on the World Bank's Ease of Doing Business index.

[38] During NRB Professional Summit 2022, Salman asked non-resident Bangladeshis to invest in the country's agriculture, healthcare and education sectors.

[39] In 2022, after a meeting with Salman, the United Kingdom's investment minister Lord Dominic Johnson expressed that British companies will be interested to explore the recycling industry of Bangladesh's ready-made garment sector.

[40] In November 2022, Salman participated in Investment Flash Mob in Tokyo, Japan and urged Japanese businessmen to assist Bangladesh in intellectual infrastructure.

[42] Salman attended Bangladesh-UAE Economic Cooperation seminar held in Abu Dhabi in September 2022 to promote trade and business opportunities of the country.

[55] During the 2010-11 share market scam, a probe led by banker Khondkar Ibrahim Khaled implicated Salman in the scandal.

[56] However, in March 2015, Salman and his elder brother were acquitted, and the cases were dismissed after final hearings, as no evidence proved their involvement in stock market manipulation.

[60] However, on 13 August, Salman was arrested at Sadarghat along with Anisul Huq, the former Minister for Law, Justice and Parliamentary Affairs, while attempting to flee by boat.

[61] They were charged as instigators in the murder cases related to the deaths of a student and a hawker during the quota reform protest on 16 July at Dhaka College.

[62] On 6 November, he was brought before the Dhaka Metropolitan Court in connection with a further murder case filed in the Mirpur Model Thana.