Image: Mt Lyell mine
Speaking in India during the week, Vedanta Resources chief executive officer and former Rio Tinto chief Mr Albanese was optimistic the Queenstown mine would restart soon.
A revived Mount Lyell would provide about 300 high-paying jobs.
The mine was placed on care and maintenance after three workplace deaths in two incidents in late 2013 and early 2014, then problems with plans to resume underground mining stymied an expected re-opening.
A new plan is being developed by Vedanta subsidiary Copper Mines of Tasmania (CMT).
"What I would like to do - and we are certainly urging the team in Tasmania to do - is to find an economic, practical and safe start-up plan, and they are working on that quite aggressively," Mr Albanese was quoted by The Sydney Morning Herald.
"There is still copper there and, as a matter of fact from an exploration geologist perspective, I would think there is probably opportunities to explore for more mineral potential in that area.
"But first and foremost, I think we have to get the copper production back up and going, and that can act as a catalyst for ongoing exploration programs."
Resources Minister Paul Harriss welcomed Mr Albanese's comments
"These comments follow the recent announcement CMT will move to the final feasibility stage of a plan to restart mining at Mount Lyell," Mr Harriss said.
"While we know there are still challenges to overcome, the government is continuing to work closely with CMT through the care and maintenance period to maximise the prospects to capture any new mineral opportunities."
Meanwhile, Indian-dominated Vedanta - already a significant player on the world stage - is set to grow through a merger with Cairn India.