England captain Kane suffered a ruptured tendon in his left hamstring on New Year's Day and is expected to be out of action until April.
Redknapp told Sky Sports: "I love Harry, what a player.
"But they got away with it last year [when Kane was out from early April until the end of the season].
"A lot of teams nowadays play without a central striker.
"I don't think I would dive in now and take somebody who, in three months time, is going to have to sit on the bench and will be surplus to requirements.
"If I was Jose, I think I would sit tight.
"They have unearthed a young kid out of the reserves this week [Japhet Tanganga], who came in and played all across the back four - he's been great.
"I am sure there might be another one there, who they might want to give a chance to.
"Chelsea have done it - there are lots of talented kids out there and they just need a chance to play."