The Millers, after a disastrous campaign, confirmed their relegation by losing 3-0 at Wigan Athletic on Tuesday night, marking their first drop into the fourth tier in 13 years.
Initially, Clark, who returned to football with Rotherham last month, has a contract with the club until the end of the season.
The former Huddersfield Town chief, 53, is not ruling out staying at the South Yorkshire outfit, who are in need of a massive rebuild with a plethora of players expected to leave at the end of the season when their deals expire.

On his time at Rotherham, he added, “It’s given me my love back, my spark back. The grass stuff and working on the training ground, I’ve loved being back in the football environment.”
On relegation, he continued: “It’s very tough. It must be very tough being a Rotherham United fan at this moment. I’m really sad for the good people at the club. There’s a big, big job ahead.”
“What I’ve walked into, it’s been a real eye-opener. It’s been sad, very sad, to have this type of scenario.
“Fans might say that it’s down to me, I had to come in, get the new-manager bounce and I had to change things. I get that. I’ve tried everything. We’ve worked so hard in terms of tactical sessions and work on the training ground, but it’s difficult.

“As I’ve said before, and as I’ve just told the players, there are too many not-so-good things here.
“We’re not a robust squad; we’re not a fit squad in terms of physical capabilities. We haven’t got the fire in our belly. When I say that, I’m not saying every single player. There are some exceptions.”
Goals for the Latics came from Jason Kerr, Huddersfield loanee Joe Taylor, and Callum Wright.
Rotherham suffered their third straight loss as their winless streak extended to nine matches.
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