Whitaker was released from his Australian Rugby Union (ARU) contract after the Super 14 season to sign for Irish club Leinster.
But with George Gregan not expected to tour, back-up scrum-half Sam Cordingley facing possible surgery on his fractured foot which could keep him out for six months, and another number nine, Josh Valentine, also on the injured list, Connolly may be forced into a rethink.
"It hasn't been discussed but I'm sure he (Whitaker) would be a consideration," Connolly told the Daily Telegraph.
"Especially if George doesn't tour and all those others are injured."
Cordingley remains hopeful he can be fit in time for the tour, claiming rest may be all that is required for his foot to heal.
"I had a CT scan and it showed up a fracture but the specialist doesn't recommend surgery at this stage," he said.
"He's told me to stay off it for a month and hopefully it settles down.
"I'm always cutting it fine but I'm quietly confident I'll be right for November."
Brett Sheehan and Josh Holmes are in Canberra for a Wallabies training camp ahead of next week's Tri-Nations clash with New Zealand, with a view to stepping in for Gregan if required.
But with both players uncapped, the experienced Whitaker may be a shock selection for the European tour, which will include games against Italy, Ireland, Scotland and Wales.