The fine Cot’s Baseball Contracts site indicates that Johan Santana only received full no-trade protection for 2008 if he finished top three in the Cy Young voting. However, I do not believe that is accurate.
There are multiple reports from good reporters with solid sourcing indicating that Santana has a full no-trade clause. There’s Kat O’Brien, Buster Olney, Michael Silverman, and Joe Christensen all saying it’s full. It’s safe to assume that Santana controls his own fate and can kill any deal. Perhaps he’d just want compensation to waive the clause, or perhaps he’d demand a record contract extension worth over $20MM per year.