England international Rose has not played since injuring himself during a 0-0 draw at Sunderland in January.
"(Rose) has started to reintegrate with first team training," the club said in a statement.
Ben Davies has slotted into the left back position in Rose's absence to good effect, although Davies was left out of the starting line-up in Saturday's FA Cup semi-final against Chelsea with South Korea's Son Heung-min preferred.
Son was guilty of giving away the penalty which allowed Willian to put Chelsea 2-1 ahead shortly before halftime at Wembley as Tottenham went on to lose 4-2.
Rose is unlikely to be considered for Wednesday's away trip to in-form Crystal Palace, when Tottenham will aim to keep the pressure on Chelsea in the title race.
Mauricio Pochettino's team are four points behind the leaders with six games to play. Chelsea are in action at home to Southampton later on Tuesday.
(Reporting by Martyn Herman; Editing by Hugh Lawson)
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