Redknapp had been hoping to land at least six players during the close season and is on the brink of achieving that target after acquiring the services of Vincent Pericard, Matthew Taylor (pictured) and Richard Hughes.
Pericard is a highly-rated teenage striker who has moved to Fratton Park on a season-long loan deal from Italian giants Juventus.
The 19-year-old marksman appeared as a substitute against Arsenal in the Champions League last term and such is the regard in which he is held, the Old Lady did not want to offload him permanently.
Pompey have announced the three signings, but the former West Ham boss has revealed that he expects another trio of newcomers to soon be winging their way to Fratton Park.
"Vincent is an exciting young player who has got terrific skill and he is not a player that Juventus wanted to sell," Redknapp told planetfootball.com.
"It will be good experience for him and as there were several Premier League clubs, and Belgian clubs, looking to take him on loan as well, I am pleased to have him.
"If he can play in the Champions League, then he can play First Division football for Portsmouth.
"If he is doing well, he will play here and Juventus felt English football would be good for the boy."
Promising defender Taylor arrives from Luton Town, although the fee has to be decided by a tribunal.
Taylor was a member of The Hatters' Third Division promotion-winning campaign, and Redknapp is hopeful he will handle the leap to a higher grade.
He added: "He's a good young player and it's a step up from where he has been playing but I am sure he will be a good addition to our squad."
Midfielder Hughes makes the short hop along the South Coast after joining Pompey from Bournemouth for a small fee.
"Richard is a former Scottish Under-21 international and he's a good passer of the ball, is strong and is a big lad," said Redknapp.
The triumvirate of arrivals at Fratton Park could be added to with Redknapp optimistic of unveiling three Premiership players on free transfers by the end of the week.
Redknapp said: "I am hoping to announce another three signings by the end of the week and that will be it.
"I am after a goalkeeper, a centre half and another central midfielder."
