The midfielder is out of contract at the end of the season and has been offered a new two-year deal to stay with Saints.
However, Rangers have been linked with a swoop for the Scotland international after failing with a bid in the summer of 2011 and Davidson is hoping to focus on playing football.
"I am enjoying playing for St Johnstone and the club has been great to me," said Davidson in The Herald. "I get on well with the manager Steve Lomas and the players.
"I have six months left on my contract and I can speak to clubs in January if anything comes up. But all I can do is concentrate on my football and leave the rest to my agent.
"We'll talk further this week. I know some of the details and it is a very good contract offer from the club. If St Johnstone said they didn't want me then I'd have to look elsewhere but it's great to feel wanted.
"The last time there was talk of Rangers it was more of a problem, even just walking down the street and going to the shops. I come from a Rangers family and I'm from a Rangers area so when they put in a bid I got a bit of stick from certain people.
"But I'll just get on with playing. It doesn't matter who you are linked with, you have to be professional enough to get on with your job."
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