Webber revealed on Tuesday that he had held talks with Ferrari, with the Italian team yet to announce who will partner Fernando Alonso next year.
The Australian's new deal with Red Bull triggered talk that Massa could be set to stay at Ferrari for another season.
But speaking through its 'Horse Whisperer' channel, the Italian squad insisted no decision has been made yet and that it is in no rush to make it.
"In Maranello, no one is in a hurry to make any decisions and that's for sure," the Horse Whisperer wrote. "Yesterday, one absolute certainty of the past few months was washed away, as we now know Webber is staying put.
"Now the most vociferous and qualified rumourmongers are taking it for granted that Felipe will be confirmed, these generally being the same voices that, not only had him down as being out of the running for 2013, but would have had us believe he would not even see out the season.
"Now coming into bloom are a whole list of possible and potential replacements, with a list of names from A to Z, something Ferrari is well used to. In truth, one letter, the "Z," seems yet to be uncovered, or quite possibly it's Zorro...unmasked."