The facility in Theobalds Park, Cheshunt, will serve as a training centre for Tesco UK staff and executives from its international operations.
Tesco has submitted a formal planning application to the local authority, Broxbourne Council, through town planning agency TLA.
The application states Tesco's intention to develop "world class training facilities" on the site. The focal point of the new facility would be a conference and meeting centre, with room for 80 bedrooms. It would replace the sports and social club currently on the site.
A Tesco spokeswoman said: "We believe this will be a very positive move for Tesco staff and for the local area." The council said it would review the application in the next month or so.