The Tottenham boss has long made it clear that he believes his Spurs squad needs some experience, having previously tried and failed to sign Everton's Phil Neville. He has also championed the difference made by free transfer William Gallas.
Parker, Given and Adebayor would all add further leaders to Redknapp's squad, but he admits the Manchester City duo are distant hopes.
"We wouldn't get Shay Given from Man City, they don't seem to want to deal with us," Redknapp said. "We have tried before to get their players. I tried to sign Craig Bellamy but they wouldn't let him come here.
"I like Shay Given but I don't know if he's fit either. He has had a bit of a shoulder problem. It has come out a couple of times, so we will have to wait and see.
"Adebayor would be difficult. I don't know if it's true but they were talking about him earning £170k a week."
Football Writers' Association Player of the Year Parker will be one of the most sought-after players of the summer, after suffering relegation with West Ham. Redknapp does not deny his interest, but he knows he faces competition.
"Scott is a quiet boy but he is a leader because on the pitch he leads by example," Redknapp said. "I'm not just saying necessarily Scott but we need to find one or two that are that type if we can.
"He is Footballer of the Year. There will be a lot of big clubs interested in him. Liverpool and Arsenal are, I hear.
"When you look at the people who have won that FWA award it's amazing. He will not be going somewhere like he did at Chelsea and play a little bit here and there. He will want to go somewhere and be the main player."