Clayton Dubilier & Rice is reportedly moving closer to clinching a $20 billion fundraising for its latest flagship buyout vehicle, people with knowledge of the matter said.

The private equity firm has so far collected around $16 billion of capital from investors for Fund XII, the people said, asking not to be identified discussing confidential information. It’s expected to hit the $20 billion target with additional commitments in the coming months, according to the people. 

Fundraising is getting tougher for private equity firms as institutional investors become more selective about which managers to back. That’s benefiting some of the larger firms with strong track records. 

Hellman & Friedman, Apollo Global Management Inc., EQT AB, Carlyle Group Inc. and Vista Equity Partners are among firms that have recently been raising new funds, according to data compiled by Bloomberg. TDR Capital has collected €4.2 billion ($4.5 billion) for its new buyout fund and could reach its €4.5 billion ($4.9 billion) hard cap in the coming months, Bloomberg News reported.

A representative for CD&R declined to comment. 

CD&R, which was founded in 1978, raised $16 billion for its last flagship buyout pool. That fund attracted investors including California Public Employees’ Retirement System, Canada Pension Plan Investment Board and Teacher Retirement System of Texas, according to data compiled by Bloomberg.