Neil Lennon remains tight-lipped after being quizzed over Celtic transfer target
Taylor's fellow Scottish international was sold to Arsenal last week for a fee believed to be around £25 million.
Celtic signed Boli Bolingoli-Mbombo to play in the left-back position earlier this summer but the club are keen to add competitions for places.
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Hide AdWhen asked about Taylor, Lennon said: "I'm not going to talk about a player if he's contracted to another club.
"I can't control media speculation about players being linked with us and players leaving the club.
"I only speak when they are sat here in front of me. I think it's very unfair on any player to talk about them when they are contracted to another club."