Struggling Zaragoza sack coach Aguirre
Cash-strapped Zaragoza, who followed several other top-flight sides into voluntary administration in June, also presented four new members of their board of directors on Friday as they seek to get their finances back under control.
"Real Zaragoza have agreed with Javier Aguirre to cancel his contract as first team coach," the club said in a statement on their website.
"The situation the Aragonese team is in required an urgent change of course, which is why this agreement was reached," the statement added.
Sports daily Marca reported that Zaragoza president Agapito Iglesias will travel to the Spanish capital later on Friday to meet Michel's agent and try to close a deal with the former Real Madrid and Spain player.
Michel's spell at Getafe ended when they decided not to extend his contract beyond the end of last season.
He took over from Victor Munoz in April 2009 and led the club to sixth and a Europa League berth the following year.
However, they only narrowly avoided relegation on the final day of the 2010/11 campaign, finishing in 16th.
If appointed at Zaragoza, he will attempt to help the club avoid a drop to the second division that would severely dent income from television rights.
Former Mexico boss Aguirre, who has also coached La Liga sides Atletico Madrid and Osasuna, was appointed in November 2010 to replace the sacked Jose Aurelio Gay and the 53-year-old helped Zaragoza avoid relegation last term.
With 16 of 38 matches played this season, they have just 10 points and are four behind 19th-placed Racing Santander.
"The players will get through this," Aguirre was quoted as saying in local media on Friday.
"I would have liked to stay to the end but I understand that these things happen in football."
In a separate statement, Zaragoza said the new board would seek to "professionalise and modernise" the club and introduce more transparency following criticism of Iglesias and his fellow directors.
Zaragoza have won Spain's King's Cup six times, the last coming in 2004, and beat Arsenal to win the European Cup Winners' Cup in 1995.