Redknapp, now manager of QPR, claimed some English players asked him to pull them out of national games when he was in charge at White Hart Lane.
England captain Gerrard called on him to name the players in question, but Redknapp who was Spurs boss from 2008 to 2012 has refused to do this.
"I understand Steven's concern but I don't want to get into naming names because it wouldn't be fair to the players," Redknapp told Sportsmail.
"Probably even (England coach) Roy Hodgson. But sadly this attitude is not unusual these days.
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"You've only got to look at how many players pull out of an international game on Tuesday and Wednesday then are running about for their clubs the next Saturday to see that this is a very real issue."
Redknapp stunned members of the England camp in Brazil on Sunday with his comments.
"When I was at Tottenham, when full internationals came around, there were two or three players who did not want to play for England," the QPR boss told BBC Radio Five's Sportsweek programme.
"I'd say, 'you're playing for your country, you should want to play'.
"(They would say) 'Nah, my girlfriend is having a baby in four weeks, I don't want to play' and that is the truth, so it makes you wonder."
Gerrard said he has spoken to one ex-Spurs player, who was "devastated" by Redknapp's comments.
"I don't know who he means. Is it five years ago? 10 years ago? We need names," Gerrard told a press conference in Rio de Janeiro.