The 23-year-old will sign until the end of the current season as he looks to get some regular first-team football and Redknapp tries to add some quality to his squad.
The midfielder has previously had loan spells at Leeds, Derby, Ipswich and Peterborough and knows Redknapp well from his time at White Hart Lane.
Despite being restricted to just four appearances since moving to Celtic, Jack Hendry insists he is constantly improving his game.
Tottenham Hotspur midfielder Dele Alli has admitted he does not welcome allegations against him of diving, although he claims to be undistracted by them.
Karen Brady 'Let me be frank. The Board takes full responsibility for our predicament'
Despite being three wins away from FA Cup glory, Mauricio Pochettino has admitted the achievement would pale in comparison to a Premier League title.
Under-fire Baggies coach Alan Pardew has demanded his senior players improve their performance and help the troubled bottom of the table English Premier League side get a win in Saturday's fixture against Bournemouth.