The 32-year-old signed a four-year deal for the Tynecastle outfit ahead of the start of the season following the expiry of his Norwich City contract.
But he admitted to PLZ Soccer there was interest from Ibrox.
Naismith had talks with Rangers but with Hearts more pressing in their need to sign the forward he took a "gamble".
He said: "At the same time there was chats going on in terms of something happening. But it wasn't something that was priority.
"Then Hearts came in and they needed to know. It was a bit of a gamble and I had to make the call."
The player has been instrumental during his time at Hearts, initially joining on loan in January 2018, albeit his Tynecastle career has been interrupted by injuries.
He missed the weekend's defeat at Celtic but it is hoped he will be back for the Hamilton game on Saturday in Gorgie.