Chelsea signed Begovic this summer in an £8million deal from Stoke.
While Courtois toppled Petr Cech as Chelsea's No 1 last season, resulting in the Czech international joining Arsenal, James believes Begovic is capable of doing the same to Jose Mourinho's current first-choice shot-stopper this term.
"Courtois won the league and didn’t concede that many goals, but he didn’t have the sort of season you’d associate with his seasons prior to that when he was at Atletico Madrid," James said at the launch of BT Sport’s new Premier League coverage.
"He (Courtois) was like Cech, he was a monster. I couldn’t wait for him to come to the Premier League and thought Cech’s record of only conceding 15 goals in a season would be under threat. But it didn’t transpire like that.
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David James believes Thibaut Courtois could risk losing his place to Chelsea new boy Asmir Begovic
"His age (is his weakness). There has to be a drop in form at that age. Maybe last season was Courtois’ comparative drop.
"Asmir is a very, very good goalkeeper. Courtois came with a massive reputation and I was his biggest fan at Atletico.
"Last season maybe it was new to him but he’s going to have to improve this season otherwise Begovic will have an opportunity to really fight for that position.
"I know historically Jose Mourinho isn’t frightened to drop key players.
"He did with Cech a couple of years ago and told him to buck his ideas up. He did with Iker Casillas at Madrid. If Asmir gets his chance he’s good enough."
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