Diame reportedly has a £3.5m release clause written into his contract at the Hammers.
"He's a good player," said Redknapp. "You'd love to have him here but he belongs to West Ham. If he has a clause in his contract, he's a player we'd like to have."
Livermore has been made available for loan in the January transfer window and Redknapp is keen to be reunited with a player he managed at Tottenham.
"I have bags of time for Jake as a player," said Redknapp. "He's a possibility - if Tottenham wanted to do something he's someone that interests me."
However, Redknapp was less optimistic over other transfer targets, saying Nicolas Anelka's wage demands would probably scupper any chances of the French striker swapping China's Shanghai Shenhua for west London and also played down the likelihood of loan deals for LA Galaxy striker Robbie Keane or New York Red Bulls midfielder Tim Cahill.
"They are top players who would improve any team but it would only be a short-term loan," said Redknapp. "You are talking about taking them for about six weeks and then you lose them at a time when you maybe have about 10-12 games to stay up.
"They are two fantastic professionals and two great players but I'm not close to doing anything with them."