The duo picked up their knocks during Spurs' 2-2 draw against Manchester City on Saturday (21 January). Alderweireld went off in the second-half with a suspected hamstring injury, while Rose played the full game, but reportedly left the stadium with his knee in a brace.
According to the London Evening Standard, the pair have flown with the rest of the team to Barcelona for warm weather training and were assessed ahead of their session on Tuesday. Tottenham play three games in the next seven days and the duo are unlikely to be risked for their first game against Wycombe Wanderers in the FA Cup.
Mauricio Pochettino recently lost Jan Vertonghen for six weeks with an ankle injury and the loss of two more regular starters will come as a big blow going into the most crucial part of the season. Kevin Wimmer stepped in to replace the Belgian for their recent clash at the Etihad Stadium, and the Austrian is likely to get a long run in the team in the coming weeks.
The 24-year-old has found game time tough to come by this season, having made just four appearances in the Premier League thus far. However Wimmer admitted that he is ready to step in and provide cover while revealing that he is hoping to emulate the quality of Vertonghen's performances thus far this campaign.
"It's not the first time I had this situation. I train every day and learn a lot from the other guys, from Toby and Jan especially," Wimmer said as quoted by the London Evening Standard. "I always try to look at what they do and when I get my chances, I try to copy them a little bit. Of course I try to do my best but it's not easy when you don't play every week. You always have to be ready as a footballer — and I am."