I have recently purchased a DELL Laptop which comes with Windows 8 Basic. Is it possible to upgrade that to PRO version with the offer.
No, it's not possible.
What is the Windows Upgrade Offer? If you buy a qualified Windows 7 PC between June 2, 2012 and January 31, 2013, you can purchase a download of Windows 8 Pro at a special promotional price that varies by region.
Already purchased a Windows 7 PC? Great, we’ve still got you covered. If you bought a PC preinstalled with Windows 7 Home Basic, Home Premium, Professional, or Ultimate on or after June 2, 2012, just go to windowsupgradeoffer.com and register.