The Republic of Ireland forward has been widely linked with a move away from White Hart Lane, having fallen down the pecking order in N17, with Bolton Wanderers, Blackburn Rovers and Fulham all said to hold an interest in the 31-year-old.
But with pre-season now underway and a move yet to materialise, Redknapp has insisted the former Leeds and Liverpool man will be given a chance to prove himself at Tottenham.
"I've said many times that Robbie's a great professional, a great character and a great lad," Redknapp told Sky Sports.
"He's still a good player so let's see what happens.
"If he doesn't go he'll be here and start on level terms with the rest of the players so it's up to him then to get in the team.
"If somebody wants to buy him and he feels he wants to move on then it's great for everybody but we'll wait and see."
Keane has failed to recreate the magic of his first spell at Tottenham since returning to White Hart Lane in January 2009, making just 49 appearances in a two-and-a-half year spell interrupted by loan stints at Celtic and West Ham.
