Sylla, 28, is out of favour at Celtic after making just nine appearances this season.
Martin O’Neill purchased the versatile Guinea international from St Johnstone in 2001 for £650,000.
Rumours are that Wolves and QPR are also interested. However, Levein’s SPL connections may swing any potential deal in favour of him.
"Next season our squad is not going to be as big as it is at the moment so the more the players can adapt the better. I have seen him play in a number of positions so he is the sort of player who would be a valuable asset to us.
"I would like to thank Martin O'Neill for letting us bring him down to have a look at him, and for him to see us, and we will just have to see what happens later on."