The 28-year-old is available on a free transfer at the end of the season, with his contract at Schalke set to expire in June.
Neustadter can play as both a defensive midfielder and centre-back, but has played 20 of his 23 Bundesliga appearances this season in defence.
German newspaper Bild reported Arsenal's interest last week, with the Gunners keen to strengthen in central defence. This has since taken added credence with The Times' report Per Mertesacker will not be offered a new contract.
Neustadter, 28, has two international caps for Germany, although the last of these came back in 2012.
The last time Tottenham and Arsenal competed to sign a player from Schalke it was over Lewis Holtby, with Spurs winning that particular battle, although his time at White Hart Lane was not a success.
Neustadter has previously played for Mainz and Borussia Moenchengladbach, and was born in Russia.
At Tottenham he would have to compete with Jan Vertonghen, Kevin Wimmer and Toby Alderweireld for a first team spot, but would represent an upgrade over the loaned out Federico Fazio.