Pellegrini took Malaga to the quarter-finals of the Champions League, narrowly losing to Borussia Dortmund in their debut season in the competition.
However the club, currently fifth in La Liga will not be able to enter European competition next season because of a Uefa ban for financial issues.
“They are currently not up to date on payments. Things cannot be promised that then cannot be met,” Jesus Martinez told Onda Cero.
“The club is not perfect, they cannot continue as they have.
“We want real solutions. This is the only concern of Pellegrini. Malaga can continue more or less as they have and to fight for between third and sixth."
Martinez added though, despite the money problems, Pellegrini would like to stay at Malaga and continue the good work he has begun, insisting there has been no contact from any other clubs.
“Undoubtedly, Manuel wants to stay in Malaga, as evidenced by what he has done and is doing. It seems that Malaga is a fairy tale," he continued.
“When we signed, he believed he could grow the club to be an alternative to Madrid and Barcelona. Now we cannot get to that level, but we can compete with Sevilla and Valencia.
“Pellegrini wants to strengthen, so that the continuity of the project is a reality - at the time it was, but now it is in the air.
“Manuel can never thank or be as happy as he has been in Malaga. He has a contract and a clause of €4 million.
“Nobody has come to Malaga with €4m asking for permission to speak with Pellegrini. Therefore we have our feet on the ground, trying to continue with the project.”