Sport Bild, a German publication, reports that Glock and Marussia have now agreed to split, despite the existence of a contract for 2013 and 2014.
The report said the news will be made official on Monday, with Glock to be quoted as saying: "I have had three great years with the team. We depart amicably.
"Now I want to meet new challenges and continue my path in motor sport."
The reason for Glock's split is almost certainly financial, with the well-funded British rookie Max Chilton already signed up to drive one of the cars in 2013.
Marussia is yet to comment.
But the mass-circulation Bild newspaper said Marussia "desperately needs money", meaning Glock's cockpit "must be sold to a pay-driver".
That report said the replacement for Glock, who earned about EUR 2 million per season, will have to pay "at least five million" to be Chilton's new teammate.
Britain's Telegraph newspaper mentioned Vitaly Petrov or Sebastien Buemi as potential candidates.
And Belgium's RTL named Jerome d'Ambrosio, the Eric Boullier-managed 2012 Lotus reserve who in 2011 was Glock's teammate at Virgin, as a possibility.
Swiss newspaper Blick wrote: "The biggest mystery is what Glock will do now? Is he suddenly on Force India's list?"
Auto Motor und Sport said he is in the running to race for BMW in Germany's premier touring car championship DTM in 2013.
BMW-contracted driver Dirk Muller said to Glock on Twitter late on Sunday: "Many congrats and welcome in the club".
Glock responded: "Ppssss ... danke".