Keane - who played under Redknapp at former club Tottenham - clinched the MVP award on the way to helping LA Galaxy win the MLS Cup.
Defoe has also worked with Redknapp during stints at West Ham, Tottenham and Portsmouth and was linked with a switch from current club Toronto FC to QPR in the last transfer window.
Redknapp has spoken of his wish to bolster his squad when the window opens in January, but stated that a move for the experienced forwards is not on his agenda.
"No [there has been no approach] for Robbie," he said. "Robbie Keane is a fantastic player, one of the best professionals I've ever come across.
"You only have to look at what he's done in America. He hasn't gone there for a holiday, he's gone there and become the best player in the league.
"He's an amazing footballer. I've never made any enquiry for Robbie, he belongs to the LA Galaxy, they aren't going to let him go."
On Defoe, he added: "No, I've never spoken about Jermain. We made an enquiry in the summer. It was too expensive we couldn't do a deal and the club wouldn’t let him go anyway.
"I've said all along if it's an expensive deal we wouldn't be able to do it. He's a good player again, but his age and everything else [makes it difficult]. The type of money the club paid for him they won't get that back I wouldn’t have thought."
Redknapp also confirmed that Steven Caulker is fit for Monday's Premier League visit to Everton.
The centre-back suffered a cut to his head after he slipped over when a selection of QPR players went for Christmas lunch last Sunday.
Newspaper reports claimed that Caulker was injured as a result of a scuffle, something the club quickly denied and Redknapp insists the issue is now done with.
"He's [Caulker] OK, he's recovered," he added. "He took a bang on the head. They went out for Sunday lunch the players, a few of them anyway, not all of them, and had Sunday lunch and Caulker fell over.
"I don't think it warranted front page headlines. Surely there's more important things in the world than Caulker falling over and banging his head?
"It was just a small group that went out for Sunday lunch. I didn't stop them doing it, they were quite entitled to do that."
