Robshaw was reappointed the Red Rose skipper yesterday, after leading Harlequins into the Heineken Cup quarter-finals.
His attention now turns to the Six Nations, with England's opening clash with Scotland looming on the horizon.
But Dallaglio, a Lions tourist in 1997, 2001 and 2005, reckons Robshaw is already the frontrunner to lead Warren Gatland's men Down Under.
"With the Lions, you need a forward to captain the team," Dallaglio told talkSPORT.
"The backs get all the glory. They don't need to be captain.
"I know Warren Gatland was of the view that Warburton is the best open-side and Justin Tipuric, also from Wales, is the second best.
"But he can't have ignored the performances of Robshaw, particularly the one against New Zealand. With every match he's playing better."
Dallaglio was not initially convinced by Robshaw as an openside flanker but he admits he has been proved wrong.
"I've changed my views on Chris Robshaw," added.
"The more I watch him and the more I see the stats from the games, I think he's turning into an outstanding seven.
"OK, he's not going to turn the ball over as much as a Richie McCaw or a David Pocock, but when they play against him they're not going to turn the ball over that much either.
"I think Chris has really blossomed into a fantastic player.
"He's leading the champion club in England, No.1 seeds in the Heineken Cup.
"He's the outstanding candidate for me at this moment in time."