Cummings in action against Rangers last month
Stubbs is expected to sign a three-year deal at the New York Stadium on Wednesday, after admitting he could never match this season's Scottish Cup success at Easter Road.
Stubbs (L) is set to leave Hibs on a high
And the 44-year-old's appointment could give Rotherham the upper hand in the race for Cummings - a reported target for Wolverhampton Wanderers and Rangers, among others.
Cummings scored 25 goals for Hibs throughout the 2015-16 campaign, but only has a year to run on his contract with the Edinburgh club.
The 20-year-old has also scored in half of his six appearances for Scotland's Under-21s, and is said to be valued in excess of £1 million.
Cummings (R) scored 25 goals in all competitions in 2015-16
It was reported earlier this month that Rangers are unlikely to pursue their interest in Cummings after the two clubs' relationship was soured by supporter unrest at last month's Scottish Cup final.
Stubbs will be keen to build on Neil Warnock's success in South Yorkshire, after the veteran boss led the Millers to safety by a margin of nine points having taken over when they were six points adrift.
Warnock turned the Millers around inside three months