Redknapp, Davenport's boss at Southampton earlier in his career, described the player as "lovely and inoffensive".
He said: "I know Calum. I had him on loan - a lovely lad, inoffensive and it's really sad to see what's happened to him and his mum.
"Hopefully they'll pull through and be okay. You couldn't meet a brighter, more laid-back lad than him."