Bale came off the bench against Wolves on Sunday to make his first appearance in six weeks due to a back injury.
Van der Vaart missed the 3-3 draw at Molineux and has not played since Spurs' 1-0 win at the San Siro three weeks ago, but looked sprightly during an open session at the club's training ground in Chigwell, Essex.
Younes Kaboul, who has been out since December with a knee injury, also trained on Tuesday morning and could be fit for a shock return against the Rossoneri.
Ledley King also took part but Jonathan Woodgate, who made his comeback from a long-term groin injury in the San Siro, did not train and looks to be out of Wednesday's showdown at White Hart Lane.
Source: PA
Source: PA