Rangers travel to Rugby Park on Wednesday night to take on Kilmarnock in the Gers' first match since the winter break, after Friday night's Scottish Cup clash against Cowdenbeath was cancelled.
Defoe, 36, has joined Rangers on an 18-month loan from AFC Bournemouth, and has caused a stir in Scottish football as one of the biggest signings made to date by a Premiership side.
But O'Donnell has sent a warning to the 57-time England international, stating that he must respect his Scottish Premiership opponents or he could turn out like Celtic flop Juninho.
"He is coming up here and he needs to respect us as well because if he doesn’t then he won’t do as well," O'Donnell said. "It is not every top player that comes up and hits the ground running.
“You’ve seen that with Celtic, they signed Juninho a few years back and he didn’t do how everyone expected him to do. It is tough. It is a tough league that poses different challenges to England but he is a top player so I am sure he has got the tools to perform."
Juninho joined Celtic after his second spell at Middlesbrough in the summer of 2004, but he managed just 22 appearances in all competitions for the Hoops. He was used out wide, rather than in the middle of the park, and left a year later.
Rangers and Steven Gerrard will be hoping of a lot more from Defoe during his spell north of the border, and Rangers look to stop Celtic from making it eight Scottish Premiership titles in a row.
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