Ben Davies could return against Liverpool after recovering from illness, with Jan Vertonghen an alternative option on the left side of the defence.
Wanyama will see a specialist next week as he continues to struggle with a knee problem, while Dembele's injury-ridden campaign is now being hampered by a fresh hip problem.
However, Pochettino stressed that the defender isn't fit enough to start against Liverpool, and is more likely to be involved from the offset in Wednesday's Carabao Cup tie at home to West Ham United.
"Now the process is to build up and get better every day". "I said, 'Yes". They said 'When we saw the starting XI... what the F?
Rose was given a warm reception by the travelling Spurs fans on Tuesday on his first appearance since criticising the north London club's transfer policy and wage structure in August, prompting suggestions he had played his last game for the club.
"It was wonderful because some people very close to us said, "Can we be honest with you?' I said, 'Yes". "His mind is clear that what happened is in the past and we need to move on".
The outlook for Erik Lamela is more optimistic.
Spurs boss Pochettino has admitted that he is concerned about Wanyama's situation.
"Everyone waits to see the shape or the system or the starting XI, and everyone disagrees".
On Dembele, Pochettino's assistant Jesus Perez added: "He had an incident in one of the training sessions (before the Real Madrid game), and complained about one of his hips and he's not able to cope with the intensity of the training".
"It's a period for us to learn a lot", Pochettino said.