The winger underwent a scan on Monday on the groin injury which has sidelined him for four weeks.
Lennon is desperate to return for the fourth-round replay away to former club Leeds, but Redknapp, understandably, is erring on the side of caution.
"It's important not to rush him back,' said the Spurs boss. 'We wouldn't take that chance.
"He'd be keen to play at Leeds but whether it's possible we don't know yet."