Rangers failed to capitalise on Celtic dropping points last weekend by playing out a 1-1 draw against Aberdeen at Pittodrie.
The Glasgow giants then squandered a great opportunity to secure a place in the Europa League knockout round when they only managed a 1-1 draw against Aris Limassol at home on Thursday night.
Rangers could need to win at Real Betis now to reach the next round of the European competition.
Thompson admitted that Clement wants to build a winning mentality and turn Rangers into a trophy-hunting machine again.
However, he is not sure that the Rangers boss has the squad to do that as the current lot do not have it in them to win consistently.
Thompson said on BBC Radio Scotland: “He is trying to make this squad winners.
“It is all about winning every competition he enters, he keeps repeating that, but can he do that with this squad of players?
“I am not sure this squad of players can be consistent winners for the football club.”
Clement has an opportunity to win a trophy this month when his Rangers side will take on Aberdeen in the Scottish League Cup final at Hampden.