Carroll became the most expensive British player of all time when he moved from Newcastle to Liverpool in a ?35million move in January.
Redknapp was also keen on signing the striker, but his price tag put the Spurs boss off and he had to wait until this month before landing a frontman, with Emmanuel Adebayor signing on loan from Manchester City.
Benched: Andy Carroll (centre) has struggled to make an impact this season
Carroll has struggled to make the impact expected of him since his big-money arrival and has scored three goals in 14 games - one of which came against Exeter in the Carling Cup.
England boss Fabio Capello has also not been impressed with the 22-year-old, recently criticising his lifestyle and admitting he would have to lose weight in order to play for England.
Redknapp was keen not to wade into a row with Capello over his comments, but was happy to make it clear that he thinks the Carroll is one of the best strikers in the league.
Redknapp said: 'I don't know anything about his personal life and whether he drinks or not. (Liverpool boss) Kenny Dalglish is the only person who knows that.
New boy: Harry Redknapp signed Emmanuel Adebayor in the summer
'If Kenny is happy with him then that's all that matters really.
'As a player, he is a real handful. He is a great header of the ball. When you go up against him you know you have had a game, that's for sure.'
Redknapp may get a reminder of what he missed out on if Carroll is selected to play for Liverpool at White Hart Lane.
Another of Dalglish's strikers, Luis Suarez, is expected to start after beginning the season with three goals in five matches.
Redknapp was also keen on signing the striker in January before he moved to Liverpool from Ajax and now regrets not signing the Uruguayan.
'We looked at Suarez,' Redknapp said.
The one that got away: Redknapp was keen to sign Luis Suarez (left)
'That was a player who we probably should have taken looking back on it now.
'The fee was ?30-odd million and that's a lot of money.
'We thought he played a bit like (Rafael) Van der Vaart as well.
'We were looking for a target man but I have seen him play up on his own and he can do that. He can play anywhere. He can do anything. He is a top-class, fantastic player.'
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