Redknapp, the favourite to take over as England manager from Fabio Capello, had said he expected to be out of action for up to five weeks after having an operation to unblock coronary arteries two weeks ago.
The 64-year-old, however, could be ready to return after missing just two matches.
"It will depend on his conversation with the medical people who will give him advice," Jordan told the club website.
"He's feeling good, he sounds good and I would think there is a possibility he will be back for the Villa game.
"The way he sounds, he's very keen and optimistic that will happen."
Redknapp and his former chairman at Portsmouth, Milan Mandaric, are due go on trial in London on tax evasion charges on January 23.
Redknapp and Mandaric, who is now Sheffield Wednesday chairman, both deny the charges.
Tottenham are currently fifth in the Premier League table, nine points behind leaders Manchester City.
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