The DotCom centre would create 70 jobs and be used to deliver goods and groceries to shoppers' homes from the Burnt Tree Island supermarket.
Plans have been submitted to Dudley Council for three extensions to the superstore, including one underneath the ground floor using some of the car park.
But the Coal Authority has lodged an official objection to the proposals because one of the extensions would be built over an entry to a mine.
It believes the supermarket giant has not provided sufficient information on how the risks would be mitigated.
The entry is one of 14 mine shaft entries within, or within 65ft, of the boundary of the property.
In a letter to council planning officer Faisal Agha, the Coal Authority's planning liaison manager James Smith said: "We raised concerns that the extension to the western side of the building would be located over recorded mine entry (shaft) 395290-038.
"We highlighted that building over or within the influencing distance of a mine entry raises significant safety and engineering risks and exposes all parties to potential financial liabilities.
"The Coal Authority has adopted a policy where, as a general precautionary principle, the building over or within the influencing distance of a mine entry should wherever possible be avoided.
"Our adopted policy clearly states that building over or within the influencing distance of a mine entry will only be permissible when a suitable engineering design is developed and agreed to take account of all the relevant safety and environmental risk factors including gas and mine-water."
A spokesman for Tesco said the application was still going through the planning process.
Councillor Ken Finch said he was aware of a history of mining on the site, adding: "There used to be a press company on the site during war time called Hewitts.
"There may have been open cast mines there too but that would be going back to the 1930s."
Tesco's application says up to 13 full and part-time jobs would be created, followed by a further 61 positions.