Redknapp junior was a Liverpool player in Gerard Houllier's first season as manager when Harry was giving Carrick his professional debut for West Ham United. Now Carrick is one of several current Tottenham stars who will face Harry Redknapp’s Southampton in the Premiership this weekend.
As Carrick's career was beginning, Jamie was withdrawn from Glenn Hoddle's 1998 World Cup squad owing to injury.
Six years later, the Spurs’ captain was preparing to finish his playing career under another leading French coach. But Jacques Santini quit as coach after only three months, with some suggesting he left because he was uncomfortable with the pressure from within the club to play summer signing Carrick in the first team ahead of Redknapp.
The rest is history - Martin Jol was given the reigns and control of team selection, and Carrick leapt in front of Redknapp in the pecking order for who should fill the holding role.
Jol was aware of Carrick's abilities from the start, and believes the 23-year-old will have a bright future at international level. However the Dutchman would like Jamie, with a modest 17 caps for England, to remain at White Hart Lane.
"Jamie is club captain and he could have a big future with Tottenham as a player or perhaps as a great coach because he is a terrific lad. All I know is he has got another year to run on his contract and he might want to play on for another couple of years," says Jol.
"But Michael is both a skilful player and passer - a very good play-maker. We have worked with him on his defensive game as well, but straight away everyone at the club could see he is one of the biggest talents in England," he adds.
Carrick has some sympathy for his former manager who has got Portsmouth fans in a rage. Since turning his back on a move there at the start of the season Carrick had to endure a melee at Fratton Park when he made his Tottenham debut there in October.
"You cannot blame Harry for taking the job at Southampton. It was a good opportunity once he'd left Portsmouth, and I think he will probably turn things around at Southampton. I can imagine what the Portsmouth fans are feeling, but these things happen in football. I am sure they will find someone else who can do a good job for them and they'll eventually forget about Harry's decision," says Carrick.
The new Southampton manager intends bringing in one or two players he hopes the younger players can look up to. The St Mary’s club is down in 19th place and Redknapp knows that keeping the Saints in the Premiership is a tough prospect. A move for Jamie wouldn't be the first time father and son have been part of the same team. Jamie was at Bournemouth for two years at the start of his career while Harry was manager.
"There's no bad apples among the Southampton players, but they're a quiet group of lads. I've got to find one or two players from somewhere who have more of a confident character. The midfield is an area we need to strengthen for sure because the blend and balance in there isn't quite right yet. I need people who will get stuck into a relegation battle, and someone I can rely on to help us out of it," says Harry Redknapp.