Rose has been sidelined since he hobbled out of Tottenham's win over Tromso on September 19 with a toe injury.
But the left-back was training with his team-mates on a foggy Wednesday morning in Enfield and could feature against Anzhi on Thursday night at White Hart Lane.
Tottenham fielded Jan Vertonghen out of position at left-back in Rose's absence, but the Belgian is expected to miss the next four weeks with an ankle injury.
Spurs are down to one fit centre-back, Michael Dawson, as Younes Kaboul and Vlad Chiriches are out with quad and knee injuries respectively.
The good news for manager Andre Villas-Boas is that playmaker Christian Eriksen is back in first-team training after his recent ankle injury.
Villas-Boas is expected to give his fringe players a run out against Anzhi as his team have already won Group K.
Anzhi have qualified as runners-up, but they are bottom of the Russian Premier League and their squad has been decimated by injury ahead of the trip to London.