The Andalusian side spent 50million euros last summer on their way to claiming fourth place in La Liga, but could be relegated and stripped of their Champions League spot if they do not pay debts owed to players and other clubs before the campaign gets under way on August 18.
And Weligton has acknowledged that the only solution could be to sell a host of first-team players, with Santi Cazorla set to be the first as he is in negotiations with Arsenal over a move to the Barclays Premier League.
He told Marca: "There are no secrets about the situation the club is in. We have had some meetings amongst the players and we continue to believe in the club.
"We know the difficult situation they are in. We are about to close the sale of one player and with this money part of the problem that we have can be solved.
"We are in an awkward situation. Everyone expected more signings, more surprises, to continue being the team in fashion.
"But, for certain reasons, including many we don't know, the chairman has now stopped investing money. We are living in a delicate moment, but there are great players here and a good bond between them.
"Everything is not lost. If we have to sell players to fix the problem then sell them and start again at zero. The club has to do what is necessary to solve the problem and it cannot wait. We cannot let the institution go down.
"If we have to sell players then we have to sell them and we can play with those that are left or those in the youth team.
"We are now expecting to be in contact with people from the club but we don't have time to wait."