"The not unreasonable allegation that Shaker Aamer makes is that both the prime minister, Tony Blair, and then home secretary, Jack Straw, must have known not just about his illegal abduction but also about his torture at the hands of the US authorities," Salmond told BBC's The Andrew Marr Show, aired on Sunday.
Salmond added that both Blair and Straw had to reveal the level of their awareness of Aamer's torture.
Aamer was the last released British inmate of the US Guantanamo Bay detention facility in Cuba. He was seized in Afghanistan in 2001 and accused of allegedly aiding the Al-Qaida terrorist group.
Aamer was handed over to US forces and subsequently transferred to Guantanamo Bay in February 2002.