Cathy Bennett says she hopes to run in Dunderdale's riding in the district of Virginia Waters in the 2015 campaign.
Dunderdale has not said whether she intends to run again.
Bennett, a businesswoman from St. John's, kicked off a 48-day tour of the province Monday.
Paul Antle, Dwight Ball, Jim Bennett and Danny Dumaresque are also vying to be named the next Liberal leader.
A leadership convention is planned for next month.