Redknapp does not expect defender King to be sidelined for too long after revealing the Tottenham defender has only suffered a grade one abductor tear.
"Ledley has had a scan. He has a slight tear in his abductor. It's not too bad," Redknapp said.
"It's only a grade one tear, which is not so bad, so it shouldn't be too long."
Bassong and Younes Kaboul are Spurs' only two fit centre-halves ahead of Thursday's Europa League clash at home to Rubin Kazan, with King joining Michael Dawson, William Gallas and Vedran Corluka on the club's injury list.
"Central defence is a big problem for us," Redknapp said.
"We are really down to two central defenders.
"The problem is that we have no one who will be back fit at the weekend so if one of them gets a knock on Thursday, we will be bang in trouble for Sunday's game against Blackburn."