QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
Ilkay Gundogan has commited his future to Borussia Dortmund by signing a new contract.
Ben Haim, 30, has been without a club since leaving Portsmouth in August and Redknapp has been running his eye over the Israel defender at QPR's training ground in west London this week.
Redknapp told a press conference on Friday morning: "I am having a look at him, he's a good defender, he's a good lad and has a great attitude.
"He looks very fit and I have let him come in and train, we will just see where we go in the next couple of weeks."
Ben Haim, who has also had spells at Bolton, Chelsea and Manchester City, has not played since Israel's 4-0 World Cup qualifying defeat against Russia in September.
Redknapp is looking to strengthen his squad next month after taking over a club rooted to the bottom of the Barclays Premier League without a win in their first 15 matches.
Redknapp has secured draws against Sunderland and Aston Villa since replacing Mark Hughes and his team face fellow strugglers Wigan at the DW Stadium on Saturday.