Calls have mounted for the former First Minister and SNP leader to abandon the show following the Salisbury nerve agent attack, which the UK Government says the Kremlin is responsible for.
It follows news that Mr Salmond's weekly radio programme on LBC has come to the end of its run and is not being renewed.
Mr Salmond told the Sunday Herald: "The idea that I would be bullied off air - whether it be on LBC or the Alex Salmond Show - by that crowd is risible. The difference is that I say what I believe to be true on air."
On Saturday, spokesman for LBC said: "Alex Salmond has completed his contract as presenter of the Sunday afternoon show on LBC. We're now discussing other projects with him."
Mr Salmond added: "I signed up to a six-month contract with LBC last September, which completed at the end of March. I have had a great time with the listeners at LBC, who are both opinionated and tremendous fun, and I really enjoyed the phone-in experience.
"I look forward to launching another project with the station which is currently under discussion."
Labour's Jackie Baillie MSP suggested Nicola Sturgeon would be "desperate for Alex Salmond to retire with some shred of dignity", while Liberal Democrat MSP Alex Cole-Hamilton said: "He take this opportunity to break with the Russian propaganda outfit."