The Scotland international, 28, is a free agent and recently spent two weeks training at Wolves, where he received a contract offer.
The forward, who has also been linked with a return to Everton, has not played since September 2010 when he picked up a knee injury playing for former club Birmingham.
McFadden's representatives have held talks with Celtic and the player has been invited to spend some time at their Lennoxtown training complex.
Speaking after Celtic's AGM, Hoops boss Lennon said: "We are hoping he is going to come up and train for a few days.
"He's a player that I've liked for quite a while, he is a very creative player and has good qualities and he is available.
"He's got goals and is a good character.
"So we are hoping that we can get something sorted out in the next few days.
"He's been out for a while but I know he has done some rigorous tests down south and passed them all.
"It would be remiss to sign him on the back of that so we will have a look at him first."