But a stumbling block could be that Leicester want to sign Taylor on loan whereas Blues would prefer a permanent deal.
Taylor suffered ankle ligament damage during pre-season and is now back available and featured in recent squads.
But the 30-year-old faces a battle to regain his place given the outstanding form of summer captures Roger Johnson and Scott Dann while Blues manager Alex McLeish also has back-up in Liam Ridgewell - currently playing at left-back - and Franck Queudrue.
Taylor's current deal expires in the summer although Birmingham have a two-year option they could exercise.
The former Blackburn player made unwanted headlines two years ago when he broke the leg of Arsenal striker Eduardo in a Premier League clash at St Andrew's.
Taylor's days at Blues looked numbered when he moved to Norwich on loan but he re-established himself at St Andrew's last season and helped the club gain promotion from the Championship.
McLeish is continuing to search for a new striker and has been linked with Kenwyne Jones (Sunderland), Ryan Babel (Liverpool), Roman Pavlyuchenko (Tottenham) and Maxi Lopez but he has so far drawn a blank.