Indian Ahsan Ali Syed, the founder and chairman of investment company Western Gulf Advisory (WGA), aquired a majority stake in Racing in January and set out ambitious goals for the north-coast club.
However, president Francisco Pernia and director general Roberto Bedoya told a media briefing on Tuesday the club's previous owners, Dumviro Ventures, and the regional government should take legal action to reverse the sale unless Ali Syed's pledges were fulfilled.
A Racing spokesman said those pledges included cash to help the club settle a debt of some 13.5 million euros with players and one of around 9 million euros with the tax authorities.
Racing also want the government, if necessary, to guarantee a loan of as much as 7 million euros as they attempt to avoid seeking voluntary administration.
"The club has shown more than enough patience," Pernia was quoted as saying in local media.
"It's starting to get urgent," Bedoya added. The government and the previous owners, both of whom are owed money by Ali Syed according to Spanish media, should step in as Racing were unable to take legal action themselves, he said.
WGA officials could not immediately be reached for comment.
Ali Syed, who failed in an attempt to buy English Premier League club Blackburn Rovers last year, told Reuters in February he believed Racing could one day compete with La Liga giants Barcelona and Real Madrid.
He said he was ready to invest whatever it took to return the club to European competition.
Bedoya told reporters on Tuesday the club was looking for a new investor who would be able to inject around 10 million euros into the cash-strapped club.
Marcelino Garcia, who coached the club to 12th place last season, walked away from his contract and this week agreed to join Racing's La Liga rivals Sevilla, accusing Ali Syed of breaking his promises.
