Pompey will pay Basle an undisclosed compensation fee for Subotic, 18, who has signed a three-and-a-half-year contract at Fratton Park.
He said: "Danijel was recommended to us and we brought him over for a few days' training. He did well and we've decided to take a gamble on him. He's one for the future and we'll have to see how he goes.
"But we still need to get some people in and it is hard. You look around and wonder who is going to loan you anybody. The only place you might get them is abroad.
"We need to strengthen out wide and up front in particular. We have just 14 outfield players here now who are capable of playing in the Premier League."
Redknapp has spent his £30million transfer budget this season and Pompey have established a place in the top 10 of the Premier League.