Redknapp in excerpts from his autobiography, which have been published this week, claimed to have received a supportive text from the Liverpool midfielder.
However, speaking ahead of England's vital World Cup qualifier against Montenegro on Friday, Gerrard said: "I can clear it up. I didn't text Harry Redknapp's personal phone, I have never had his personal number.
"But I am a big fan of Harry's and close friends with Jamie (Redknapp's son, a former Liverpool and England midfielder).
"I had a conversation with Jamie round about that time when Harry was on everyone's lips. He was the favourite and it was only a matter of days before he was going to be manager.
"I said to Jamie on the phone 'send the best to your dad and, if he gets the job, we'll all back him and we'll support him'.
"Very soon after that, the FA decided that Roy Hodgson would be the next manager and I think, from the first conversation I had with Roy, I tried to back him and give him my best, and I was absolutely delighted he got the job.
"I've worked with him before, he made me captain, and I think I've played my most consistent football under Roy, so I've got a lot to thank him for."
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