The entire team and coaching staff made the threat on Monday in protest over unpaid wages and the way the unpopular Levin and his team are running the financially troubled club.
Santander are 3-1 down from last week's first leg at Sociedad's Anoeta stadium in San Sebastian and their chances of making the last four and setting up a meeting with record winners Barcelona are remote.
"The squad decided on something on Monday which they announced publically and they still think exactly the same way," Luis Rubiales, president of Spain's players' union (AFE), told reporters after meeting with the players on Thursday.
"If the current board has not resigned by the time of the match (2000 GMT) they are not going to play," he added.
Rubiales warned the players that refusing to play could have legal consequences but said they had the union's full support.
"The players have more than enough legitimacy. I do not have words to describe everything they have had to put up with and how this inept board has got them into this situation."
Levin has shown no sign of bowing to the players' demands and was quoted in local media on Thursday as saying he intended to be in the VIP tribune for the match.
"We will try to find a consensus between all parties so that the game can go ahead," he added.
Santander have fallen on hard times since they were taken over in January 2011 by Indian businessman Ahsan Ali Syed.
Ali Syed promised to invest in the squad and said Santander could become a "third force" in Spain to challenge Real Madrid and Barcelona.
However, they were relegated from La Liga at the end of the 2011-12 season after finishing 10 points adrift at the bottom.
Ali Syed disappeared from view and the club's crisis deepened as they dropped down to the third tier (Segunda B) at the end of last term.
The future looked bleak after a capital increase in October designed to save them from ruin flopped and had to be abandoned and they remain in bankruptcy proceedings.
(Reporting by Iain Rogers, editing by Justin Palmer)
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