Kudus was absent from training on Monday with a knock and subsequently played no part in Spurs’ 4-0 Champions League win over Copenhagen.
Asked after the game for an update, Kudus said: “It's getting better.”
Frank did not go as far as ruling Kudus out of the visit of United on Saturday lunchtime, but the forward remains a doubt.
Dominic Solanke remains sidelined and Frank hopes to be able to call upon his striker later in November, following the upcoming international break.
The striker has been restricted to three substitute appearances this season, all of which came in August, before undergoing surgery on his ankle.
The Spurs boss added: "The international break is the big decider there, two weeks to push him with the big steps.
“He's going forward. After the international break is what we're aiming for. It's important to get it right so he's out there and can help the team. We need him back."