The former Adelaide forward was banned for the first 11 games of the 2013 season after the Crows' salary cap scandal.
GWS had maintained their interest despite Tippett's ban, while Sydney are now favourites to secure the services of the 25-year-old.
But the Giants, who have the first pick in the draft, said in a statement on Wednesday they were unable to pay Tippett what he desired.
Giants chief executive David Matthews said: "Internally we established a value for Kurt Tippett based on his capabilities.
"And whilst we were hopeful, his terms submitted this week confirmed that we are simply not in a position to pay what he wants, particularly for a player who will miss most of the year through suspension.
"We are committed to developing a strong culture and playing list and also retaining that talent as we have done by signing several players to long term agreements.
"In players like Jon Patton and Jeremy Cameron we believe we have the nucleus of an exciting forward line in 2013 and beyond."We will continue to look closely at talented and mature players who become available and have an opportunity to add to our list at next week's pre-season and rookie drafts."