Former Argentina boss Marcelo Bielsa has been touted as a successor to Heckingbottom, but Evans believes that the Whites should consider coaches with Football League experience, such as the Aston Villa boss or the former Ipswich Town manager.
"They're perhaps going to an Argentinian (Bielsa)," Peterborough United boss Evans told Sky Sports News. "I think his reputation in the game on a worldwide basis is phenomenal. But will he know what it's like going to the New York Stadium in Rotherham on a Tuesday night? I'm not so sure.
"But I'm looking at Steve Bruce and Mick McCarthy - English managers with track records of getting out of the Championship - and why are they not knocking on those doors? You would think the Leeds fans would be ecstatic if one of them is appointed.
"The British guys know the league and they know how to get out of it. Sam Allardyce has just come out of Everton - he must be another strong candidate. But you have to empower those guys. I'm not so sure with the sporting director and owners at Leeds that you're going to be empowered to do your job."
Leeds mounted a playoff challenge in the first half of last season but ended up finishing 13th in the table.