The full-back, who criticised Spurs' transfer and wage policy in an interview in August, was left out of the matchday squad for the 2-0 defeat to north London rivals Arsenal on Saturday, after which Pochettino was forced to deny there was a feud between them.
The England international has struggled to dislodge Ben Davies from the team since returning from injury and he has been linked with a possible move away from the club, with Manchester United reported to be interested.
Pochettino, however, says there is no problem between him and Rose and will be happy to include him against Dortmund if he can prove his fitness.
"He's doing well," he told a news conference. "The training session on Saturday was tough for him. He will now train with the group and we'll decide if he will play.
"I cannot speak about rumours. If you were to ask me if Danny Rose is here and do we have problems, I say no. No issues."
Spurs secured their place in the last 16 with a 3-1 win over Real Madrid on matchday four and they will guarantee top spot in Group H with a victory at Signal Iduna Park, or if they match Madrid's result against APOEL.
Pochettino insists the defeat to Arsenal should not detract from their continuing progress and even suggested the criticism of their performance could prove to be beneficial going forward.
He also again pointed to the performance of referee Mike Dean as a key factor in their loss at the Emirates Stadium, having criticised the officials after the match for not sending off Granit Xhaka and for allowing the Gunners' goals to stand despite debatable free-kick and offside decisions.
"Our project is a medium to long-term one," he said. "Our project is to win. I am happy that people criticise us sometimes because it means people expect more from us. That is important to put the pressure on, more than we do.
"We are so calm. We know very well that, from two years and a half ago, we improve in every single aspect. Every team in the top six struggles against each other.
"When you lose, always you try to analyse and then try to improve what was wrong. It's true that there were many decisions in the game that were decisive. When you watch again, some actions like Xhaka on [Moussa] Sissoko and Dele Alli it should be Arsenal with 10 men. Sometimes you need luck to win.
"A year ago, we were in Monaco and we were out of the Champions League. In the Premier League, we've made the second-best start since 1992. We're very disappointed because [in] the last game, the expectation was different. But we need to move on."