DBCC CHECKDB error - Write to sparse file failed due to lack of disk space

The situation:

• 1900 GB data warehouse database. 10x 190 GB data files, located on the same (virtualized) drive.
• About 30 GB free space left on that drive.
• Running DBCC CHECKDB on this database (in the off-peak hours) eventually results in an error: "Write to sparse file XXXXXX failed due to lack of disk space." Running it with PHYSICAL_ONLY works ok.

So, I guess there's not enough space left for the internal database snapshot which is used by DBCC CHECKDB to run the checks? But, is there a way to getan estimate of how much space is needed to complete the check? ESTIMATE_ONLY option is intended for TEMPDB space usage estimation, correct? There are no problems with tempdb, so that doesn't help.

Thanks!