The 21-year-old is out of contract after leaving Dynamo Dresden when his contract expired on June 30.
Arsenal had reportedly earmarked Schubert as a potential challenger to Bernd Leno between the sticks.
Reports in Germany, however, claim they have been beaten to the punch by Schalke.
Sport1 claim Schubert has signed a four-year contract and will be announced today.
Schalke appear to have won the race because they plan for Schubert to become their first-choice goalkeeper
According to Sport1, Arsenal promised the stopper that he would play in the Carabao Cup.
But, after holding several rounds of talks, Schubert reportedly cancelled a move to the Emirates Stadium.
The Independent reported in May that Arsenal were so confident the Germany youth international was in the bag that they contacted Championship clubs and German teams about sending him out on loan next season.
Schubert rose through Dynamo Dresden’s youth ranks before establishing himself as the club’s first-choice goalkeeper last term.
He made 31 appearances in Bundesliga 2 as the east German club finished 12th in the table.
Despite his lack of top-level experience, Schubert has represented Germany at every age group from Under-17 to Under-21.
Schubert was whistled by Dynamo Dresden fans at his farewell appearances at the Rudolf-Harbig-Stadion in May.
Arsenal were reportedly alerted to his potential by former head of recruitment Sven Mislintat.
Emiliano Martinez, who finished last season on loan at Reading, is likely to play second-fiddle to Leno in the upcoming campaign.
But Arsenal legend David Seaman believes an experienced stopper is needed to provide back-up to Leno.
“I think they should be trying to get a more experienced keeper in as [Bernd] Leno’s number two,” Seaman told Football.London.
“I know they’ve got some really talented young keepers in Emi Martinez, Deyan Iliev, Matt Macey and Arthur Okonkwo, but I just think they could do with an older number two. Those lads are real talents but they’ve not got an awful lot of experience at the top, top level.
“It would be a big step for them to come in and be Leno’s number two in the Premier League after being on loan or playing for the U23s.
“I don’t think they need someone like Schubert as Leno’s number two either – why not look at Joe Hart or Jack Butland as a number two?
“They have loads of experience. That’s the sort of quality they should be looking at as the club’s number two at the moment.”