Belgium international Dembele suffered a foot injury in the 1-0 defeat to Manchester United last Sunday (11 December) and was replaced by Harry Winks at half-time. He subsequently missed the 3-0 win over Hull City on Wednesday –but a return could beckon this weekend.
Janssen, meanwhile, has missed the last four league games due to an ankle injury. However, having returned to full training, he could be considered for visit of the Clarets.
Pochettino told a press conference on Friday: "Mousa Dembele we need to assess tomorrow and Janssen is the same. He is improving. We need to see how they are."
Lamela, meanwhile, has not played for the club since late October due to a persistent hip problem. The former Roma star was also given permission to return to Argentina for personal reasons earlier this month.
The 24-year-old is now back in North London but is at least a week away from a return. "Lamela is improving every day but he is still out. We are happy with his progress."
Tottenham have also announced they have reach an agreement to extend Luke McGee's loan spell at Peterborough United until the end of the season.
Prior to the arrival of Tottenham's third-choice goalkeeper Pau Lopez during the summer transfer window, McGee, 21, was allowed to join the League One side on a loan deal that was initially set to expire in January.
But the shot-stopper is now set to spend the rest of the 2016-17 season at the ABAX Stadium, where he has been named the club's player of the month two months in a row.