Shittu is a free agent after negotiating his release from Bolton Wanderers before the transfer window closed earlier this week and is currently on international duty with Nigeria.
A Celtic insider told The Herald: "Shittu is a player of considerable experience and he has a bit of pace, which is missing from the heart of the defence.
"It is no secret the club targeted other defenders during the transfer window. Shittu is an option because he is a free agent.
"The player has explained he will make a decision early in the week, so it will depend on what other offers he has on the table and the financial package the club are willing to offer to him."