Clement has claimed that he is looking to do some business in the January transfer window and bring in the right players if they become available.
Rangers are prepared to back the new manager in the winter window despite spending relatively heavily in the summer.
Clement has always been insistent that players will get a chance to prove themselves to him and Hartson also feels he is yet to make up his mind about a number of players in the squad.
He expects Clement to give all the players an opportunity.
The former Scottish Premiership star believes that the massive clear-out will have to wait until the summer as Clement will likely need more time to assess everyone.
Hartson said on the Go Radio Football Show: “What I took from the interview today with Philippe Clement when I watched him speak, is that there are still players at Rangers that he is not quite sure about.
“He is willing to give everybody a chance or an opportunity.
“Obviously, he is on the training ground every day, but I am sure that in his own mind, there will be one or two that he will maybe let go out of the door.
“He still said that everybody has got a point to prove and doesn’t want to make sort of urgent decisions on people until they have had the chance to prove themselves.
“That’s in January so he may well look to go through to the summer and offload some.”
All eyes will be on what level of backing Clement gets from the Rangers board in January.