Sports dailies Marca, As and other media all said that owner Sheikh Abdullah Bin Nassar Al-Thani - a member of the Qatar royal family - wants to sell up after only two years and is in talks with several interested parties.
"It's impossible to ignore what's going on," defender Weligton told a news conference after training.
"There are kids who play with my son who are asking me about it, who are crying, who ask if the team is going to be relegated to Segunda B (the third tier)," added the Brazilian.
"It's a difficult situation to deal with after everything that has happened, the big signings, the big player presentations.
"We were all expecting more signings, more surprises, believing that the team would continue to be in fashion. But now we don't know why all this has come to an end."
Al-Thani bought the Andalusian club for £28.5 million in June 2010 and heavy investment in players helped them finish fourth last season and secure a place in the Champions League playoff round.
However, financial problems at the club have cast doubt over his commitment and he and his representatives have been conspicuous by their silence in recent weeks.
The club published a brief statement on its website later on Thursday, saying it had "started a process of internal restructuring".
This would help adapt to UEFA's Financial Fair Play rules, which are designed to prevent clubs spending more than they earn.
The restructuring was aimed at "guaranteeing the self-sufficiency and sustainability" of Malaga, the statement said.
"This process, which does not mean some kind of investment by the current owners is rejected, will include some changes in the current organisation which will strengthen the club for the future," it concluded.
Malaga's best player, Santi Cazorla, did not join his team mates for training at the Rosaleda stadium on Thursday, raising expectations the Spain midfielder is poised to jump ship, possibly to English Premier League side Arsenal.
Other players including French midfielder Jeremy Toulalan have also reportedly threatened to leave.
Weligton, who said the players had held meetings to discuss the situation and were trying to get concrete answers from the club, appeared to confirm that Cazorla was on his way.
"It's clear to us that we are about to close the sale of a player and with the money we could resolve part of the big problem that we have," he said.
"This situation cannot be maintained and we'll play with the players we end up with, with players from the youth team or whatever it takes.
"We still have confidence in the club, we know the problems there are and we know there are people trying to find solutions."