Ray Gosling, 70, revealed last night that he had smothered the unnamed partner as he lay in hospital "in terrible, terrible pain".
A spokeswoman for Nottinghamshire Police said the force had not been aware of the issue until the broadcaster made his revelation on BBC East Midlands' Inside Out current affairs programme.
She added: "We are now liaising with the BBC and will investigate the matter."
The BBC said it would "co-operate fully" with a police investigation.
Gosling said he was not "making a cause" of assisted dying but said there was a case for changing the law.
He told the Inside Out programme it was "time to share a secret that I have kept for quite a long time" as he revealed his role in the death of his former lover.
Gosling said: "In a hospital one hot afternoon, the doctor said, 'There's nothing we can do', and he was in terrible, terrible pain.
"I said to the doctor, 'Leave me just for a bit' and he went away.
"I picked up the pillow and smothered him until he was dead.
"The doctor came back and I said, 'He's gone'. Nothing more was ever said."
Gosling, a freelance filmmaker of hundreds of radio and TV documentaries, said he had no regrets about his actions, adding: "When you love someone, it is difficult to see them suffer."
Oliver Luft writes for Press Gazette