The supermarket giant heard pitches from a number of agencies this week but is yet to make an appointment.
Tesco has a long tradition of running high-profile CSR activities, particularly its vouchers-for-schools campaign. But it has also come under fire from campaigners for years for forcing the closure of local shops.
Insiders said Tesco's CSR focus was moving up another gear with last month's appointment of Tim Mason to the role of deputy CEO. Mason will have the additional responsibility for branding, company values and climate change.