Speaking on talkSPORT, Redknapp said: "Great night for Tottenham to finally win a trophy. Fantastic for Spurs. Great that we've finally finished the season with something to be happy about.
"I wouldn't know either way whether Ange will keep his job or not. I couldn't call it either way. It's going to be a close one, I think.
"When you're sitting fourth or fifth from bottom of the table, it's certainly not that that's going to come into into the chairman's thinking."