The Kilmarnock striker, 20, has been targeted by both clubs ahead of the new campaign, with Rangers already failing with a £450,000 bid and Celtic also confirming their interest in the SPFA Young Player of the Year.
With his future still uncertain, Naismith confesses it has been hard to think of anything else this summer.
But he has vowed to give his all for Kilmarnock until he is in a position to commit himself to another club.
He said: "At the start, it was hard to get away from it all. It kind of took over the rest of my life in the last month.
"But I've let it go to the back of my head now. It's not worth worrying about it all.
"I learned not to think about it so much while I was away and get the rest that I need."
He added: "I have had to grow up a bit with all the speculation. Maybe I was a bit naive when I was younger, believing everything in the papers.
"Until someone from the club tells me otherwise, I'm a Kilmarnock player."
An important part of Naismith's learning curve was last year's trial at Arsenal.
The youngster was invited to train with the Barclays Premier League giants at the beginning of the campaign, sparking huge media interest.
Nothing came of Arsene Wenger's interest, and Naismith has since ruled out a move south of the border for the time being, but he says the experience with the Gunners has helped him mature over the last season.
"It was the first bit of serious transfer talk around me and it was just a hectic week," he said.
"It got on top of me but I learned to deal with it and I showed in the last six months of the season what I'm capable of.
"It has nothing to do with not wanting to play in England just now.
"I'm not going to say I wouldn't ever like to play in England, it's just that I don't think I'm ready just now and I don't have as much experience as I would like going down there.
"That's the only reason."
That leaves just two options - Celtic and Rangers. Asked how he feels a move to either of the Glasgow giants would change him, Naismith said: "To be honest, if I was to move to one of the Old Firm, it's not going to change my lifestyle.
"I'll still be a quiet guy who gets on with his job. I'm not one for the limelight.
"Obviously, my life would change in terms of being recognised a bit more.
"But it would be my decision to make the move and, if you make the move, you have to deal with the issues that come up."