Rangers lifted the first domestic trophy of the season on Sunday when they beat Aberdeen in the Scottish League Cup final at Hampden Park.
The Glasgow giants are also just five points behind Celtic in the title race with two games in hand and have reached the last 16 of the Europa League.
Rangers are expected to back Clement with some funds in the winter transfer window for new signings but Thompson believes that he does not need to bring in several new faces.
The former Rangers star believes that once the injuries clear up the squad will look in better shape and the Belgian can focus on bringing in personnel for specific positions in the squad.
Thompson said on BBC Radio Scotland: “If you are looking at Rangers where they need to strengthen in January, it’d be fairly obvious to suggest that a centre-forward would be high on their list and I still feel they are short in wide areas.
“Once he gets his full squad back together – [Nicolas] Raskin, [Tom] Lawrence – all these guys back together then I think certainly he doesn’t need to go out and make wholesale changes in January.
“What I think is more important is that he brings in key players in positions and he’d already know what those positions are and where he wants to strengthen.”
Rangers will have to focus on league commitments on Wednesday night when they host St. Johnstone at Ibrox.
