Hutton made a dream comeback in what was his first Spurs appearance since January on Saturday, coming off the bench and winning the equalising penalty before scoring his first goal for the club to seal a 3-1 victory.
The 25-year-old's White Hart Lane career looked to be under real threat last season when he was allowed to join Sunderland on loan.
The Black Cats also tried to make the move permanent but failed to meet Spurs' valuation of the Scotland international, who cost a reported £9million from Rangers in January 2008.
Hutton's time in north London has been blighted by a succession of serious injuries, while he was also implicated in the infamous 'Boozegate' affair while playing for Scotland 18 months ago.
But Tottenham boss Redknapp has assured him he still has a big future at the club if he reproduces Saturday`s attacking performance and improves his game defensively.
"It the kind of form he's capable of," Redknapp enthused.
"I spoke to him during the week and he's a great attacking full-back. I said to him he needs to concentrate a little bit more defensively and, if he does that, he's got everything.
"He's a great athlete; when he gets forward, he's got unbelievable pace. He's aggressive, he's quick, it's all there.
"It's up to him to push on now. Let's hope he continues to do that."
Source: PA