The FA has reiterated the next England boss could still be foreign.
"I would expect Harry to make a long list [for the England job]," Horne told BBC Radio 5 Live's Sportsweek.
The FA had said in August that the next national manager would be English.
But in October Trevor Brooking, the association's director of football development, said that availability and suitability and not necessarily nationality would be a factor in who replaces Italian Capello.
How highly do you rate Redknapp? Horne also revealed no process had yet been discussed for appointing Capello's successor.
"[Capello] is there till 2012 which gives me 18, 19 months to prepare for that process," said Horne.
"It is not a policy decision that [the contenders] would be English. It is an absolute preference for certain individuals. It is not yet a board decision.
"We thought about this long and hard when we got Fabio Capello. We got the right man for the job and that is what we will do again.
"I will be finalising the selection process criteria during the first few months of next year for internal discussion."
But with Redknapp's Tottenham side currently enjoying a fine season in the Premier League and Champions League, his stock is rising within the FA.
"Harry Redknapp is a great manager," added Horne.
"Tottenham are playing great football and to qualify well for the Champions League knockout stage from a position of being fourth favourites in the group is huge testimony to that."