Rush said talks would with Redknapp would continue on Monday evening.
He added: “Harry came to the training ground and met Darren and myself and we had a discussion and are looking at bringing him in an advisory role
“It was Darren’s idea. It is a short-term coaching role to provide support for the rest of the season. It is a defined time for the next eight weeks or so.”
Former West Ham winger Redknapp began his managerial career with Bournemouth in 1983 and spent nine years with the Cherries and then seven years with the Hammers from 1994.
Since then, he has twice managed Portsmouth, winning the FA Cup in 2008, and has also been in charge at Southampton, Spurs – where he guided the club to Champions League football for the first time – and most recently QPR.