Alan Stubbs believes Neil Lennon would be "a good choice" to replace him as the manager at Hibernian.
"He's got great experience, he's obviously a good man manager," Stubbs told BBC Scotland.
"It tells you about the ambitions of the club and I'm sure Hibs will be talking to other high-profile people."
Stubbs, also 44 and a team-mate of Lennon's at Celtic in season 2000-01, chose to leave Hibs less than two weeks after guiding them to a first Scottish Cup win in 114 years.
And he thinks the Edinburgh club will move swiftly to fill the vacancy.
"I wouldn't be surprised if we hear about a new appointment this week," said the former Everton and Celtic defender.
Stubbs failed to gain promotion for Hibs during his two seasons at Easter Road, twice losing out at the play-off semi-final stage.
However, he is backing his successor to lead the club back to the top-flight next season.
"I'm leaving behind a great bunch of players," said Stubbs. "It was a privilege working with them.
"I fully believe they will go on and win promotion."
Stubbs will now begin assembling his Rotherham squad and admits he will consider recruiting from Scotland, but he has pledged not to raid his former employers.
"I'd like to, but I wouldn't," he said when asked about the possibility of signing anyone from Hibs.
"There are players there I would take, but out of respect I won't be returning.
"There are certainly players in Scotland who would embrace the Championship, but I won't give you any names."
Stubbs is happy he could deliver the Scottish Cup for Hibs after such a long wait and 10 lost finals since 1902.
"It probably didn't sink in for five or six days," he said of the 3-2 success over Rangers at Hampden. "I'm glad to be leaving on the back of such an amazing win.
"That Saturday and Sunday [the cup parade through Edinburgh] will stay with me forever.
"It's such a fantastic club and I thoroughly enjoyed my two years."