The 28-year-old front man was linked with the Ibrox outfit earlier in the summer, with North End issuing a 'hands off' message.
However, the speculation has started again, with Scottish Premiership side Rangers said be considering making an offer to try and lure him to Glasgow.
PNE sources say there has been no bid for Garner and they want to keep him at Deepdale.
Rangers have done a lot of their recruitment south of the border in recent months, with manager Mark Warburton and head of recruitment Frank McParland both English.
Garner made his 150th appearance for North End in Tuesday night's 1-0 win over Hartlepool United in the EFL Cup.
He has scored 57 goals in a Preston shirt, 49 of them in the league.