Carroll has shone on-loan at West Ham United.
But Keegan told the Mirror: "I think it's pretty obvious Brendan doesn't want to [have Andy Carroll back].
"The first thing managers normally do is take a look at the players and then if he wants to loan him out then loan him out at Christmas.
"He got rid of him straight away, so maybe that tells its own story.
This comes despite the former Newcastle boss' doubts over Liverpool's striking options.
"I'm not sure about forwards because they've got a lot of them but they're all the same! They're all small, quick guys.
"They need what I'd call a 'proper centre-forward', which none of these are, not Sturridge, Borini, Coutinho - these are all what I'd call second strikers at best."