Neither player has had a role to play for Mauricio Pochettino's side this season with Lamela's spell on the sidelines dating back to October last year. The Argentina international underwent surgery on both his right and left hip in the spring with his manager revealing earlier this season the forward is now in the "advanced stages of his rehabilitation," initially pencilling in a return this month.
According to the Evening Standard, there is an "outside chance" of that timetable being adhered to, with the Carabao Cup tie against West Ham United on 25 October a possible return date. November could prove to be a more realistic option however.
Rose is also nearing his return having not played since 31 January where he suffered a season-ending knee injury away to Sunderland. The England international also underwent surgery in May but returned to full-training on Wednesday as he nears his comeback.
Tottenham have also been without influential midfielder Victor Wanyama since late-August due to a troublesome knee problem. The Kenya international is also to return to first-team training this week and is unlikely to be ready in time for Saturday's Premier League clash with Bournemouth or the Champions League trip to Real Madrid, but has targeted a return against Liverpool on 22 October.
Moussa Dembele has also been a recent absentee, missing the club's last three games prior to the international break with an ankle problem. The midfielder underwent ankle surgery to try and rectify the long-running issue during the summer which is still giving the player trouble, although Pochettino does not think another operation will be required."
The Standard report the Belgium international has not returned to full first-team training with the rest of the squad and is unlikely to feature against Bournemouth on Saturday.