Redknapp has already captured striker Jermain Defoe during the transfer window and has been linked with a number of other Pompey stars.
"I would have gone back and taken Glen Johnson but I didn't want to get involved and cause problems," he said in the Sunday Telegraph.
"Defoe was different, they wanted to sell Defoe. Man City were in for him, there were a few clubs in for him.
"He was up in the open market but they didn't want to sell Johnson.
"I've not gone near him. They wanted to keep him and he's signed a new contract, which is great for the club."
Redknapp, who has also been linked with midfielder Niko Kranjcar, maintains that he will only pursue a Portsmouth player if he is up for sale.
He explained: "I wouldn't bother going for Kranjcar. Unless they want to sell them, I won't go, I wouldn't do that.
"Somebody said I was disrespectful to Tony over Defoe but I wasn't.
"I wouldn't cause any problems for Tony Adams or (chief executive) Peter Storrie or the club."