The Scot left his post after three-and-a-half years when differences were exposed between himself and chairman Tony Stewart during a routine meeting between the pair.
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Evans, whose side beat Birmingham at the weekend to move out of the Championship drop-zone, delivered two promotions for the Millers and kept them in the second tier last season.
Stewart and former Crawley manager Evans aren’t commenting for now.
Other early contenders include Neil Redfearn, Jimmy Floyd Hasselbaink, Brian McDermott and Nigel Clough.
First-team coach Eric Black has been appointed interim boss as the South Yorkshire club begin their search for a new manager.
Brentford recruited former Excelsior manager Dijkhuizen in the summer following the controversial departure of Mark Warburton.
Rotherham are inviting applications and have two weeks after the Clarets clash to appoint a new man before they resume Championship action.
Asked what is next for Steve Evans he replied, ‘My ‘phone has been lively since the news broke but I’ve no desire to talk about which clubs have been in touch’.
“We had our normal meeting as we have had on a daily basis for three-and-a-half years”.
Back in the Championship after a nine-year absence, United won their fight for survival with a game to spare.
As is to be expected in such a long list, there were hits and misses in terms of transfers but the inspired additions of Kieran Agard, Kari Arnason, Craig Morgan and Lee Frecklington in Evans’s first full season did lay the foundations for the tremendous success that followed.
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The Millers also added: ‘The meeting was at all times positive, constructive and straightforward. “Rotherham United Football Club will always welcome Steve and Paul whether as an opposition management team or as supporters of our fantastic football club”.
