The Madrid-based club is in dire financial straits and their owners, the Ruiz-Mateos family, last month applied to put the business into administration. They have also opened negotiations with prospective buyers.
"We aren't ruling out refusing to travel to Valladolid. It's a situation no one in the squad wants but it is an alternative we have," team captain Michel told reporters on Wednesday.
"We feel we are on our own. No one is helping us. The league wants more money (referring to the professional football league's failed attempt to postpone this weekend's matches over television revenues) but the players don't get paid."
Rayo moved to the top of the standings with a 1-0 victory over their closest rivals Real Betis on Sunday, in a game where home fans protested against the club's owners.
"We've gone close to a year without being paid," Michel added.
"At the last meeting with the owners they said they would try to do something from ticket sales, but we haven't seen a euro. We feel as though someone isn't being straight with us.
"We are very sorry for the fans. We have been told that if a sale happens it will take two months to resolve because of the debts. We can't carry on like this. We want the (Ruiz-Mateos) family to do something to pay the team.
"We are talking about the leaders of the division. We deserve more respect." Rayo are top by two points with 11 games left to play, and are scheduled to visit Valladolid on Saturday.
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