He hasn't played for City this season and is out of contract in the summer. The 31-year-old Greenock-born centre back was to go on trial at the Scottish Premier League side but a calf injury blocked the move.
However, Jeffries has revealed that if Anderson gets fully fit then he would be keen to take the player back north of the border.
He said: "John is a player I'm interested in signing but I want to see him prove his fitness first. If he can do that, then we'd be prepared to offer him something."
City are not expected to demand a fee if the transfer goes ahead.