Colin Maclachlan, 42, from Edinburgh, wrote about how he had killed "two or three" mortally wounded enemy soldiers in Iraq in 2003 in a new book.
Killing mortally wounded soldiers is against British military law and the Geneva Convention.
The MoD would not comment on the reported military police inquiry.
Sgt Maclachlan said the killings took place on the Syrian border in March 2003, where an SAS squad fired rockets at enemy units. After the attack Mr Maclachlan discovered two Iraqi soldiers who had been disembowelled and another that had lost three limbs.
Sgt Maclachlan, who appeared on the Channel 4 show SAS: Who Dares Wins, said that the injured soldiers were "pleading for us to do it".
He wrote: "Special Forces operatives quickly put them out of their misery, rather than leaving them to die slowly and in agony."
It is part of a new book on SAS Who Dares Wins: Leadership Secrets From The Special Forces.
Speaking to the Mail on Sunday, the former soldier said he was informed of a military police investigation by email.
He added: "Our motives were entirely humane. I'll happily go to court, I'll happily go to jail, if you think I've done wrong. But people should put themselves in my position first. Walk around in my boots, then judge me."
Although the MoD would not comment on Mr Maclachlan's accusations, a spokeswoman said: "Credible allegations of criminal behaviour will always be investigated properly."
A former SAS sergeant has said he is being investigated for murder after admitting he shot dead enemy fighters in what he called a "mercy killing".