Templeton was freed by Rangers manager Mark Warburton at the end of his Ibrox contract.
Templeton has not played since August 2015 because of a ligament injury and was released at the end of his Ibrox contract in June.
Prior to his spell on the sidelines, the former Heart of the Midlothian player scored 27 goals in 88 Rangers appearances, helping the Glasgow giants to two promotions.
Consequently, Templeton has no shortage of suitors since becoming a free agent, with Bradford City and Raith Rovers both linked with moves following his release, and the Citizens are the latest club to register their interest.
But the 27-year-old, it seems, is still not ready to return.
"It was worth a try," said City boss Gary Jardine, as quoted by the Scotsman.
"We could have done with David’s experience and playing with us could have led to David stepping back up the way.
"However, we were told that David was not up for playing yet, so that was that for us."
Rangers paid a reported £700,000 to land Templeton four years ago, after the Glasgwegian had impressed for both Stenhousemuir and Hearts.
Templeton was coached by Raith manager Gary Locke at Tynecastle, and played under Bradford boss Stuart McCall at Ibrox, which would explain the pair's interest.