Foss told reporters he did not receive a direct message from English that he was facing demotion.
And he had already been selected to stand again in Tukituki.
But he conceded his decision was made after meeting his leader, when issues such as the pressure on ministerial posts was discussed.
Foss had already been moved from the Cabinet to outside Cabinet.
Lotu-Iiga lost the Corrections portfolio a year ago. But there was less certainty English would demote him.
However, he and his wife have recently adopted a baby boy and he cited family reasons.
Auckland councillor Denise Lee (formerly Krum) is thought to be interested in seeking the nomination for National in Maungakiekie.
She was elected in October for her second term as the Maungakiekie-Tamaki councillor.
Former Prime Minister John Key will retire next year and former Auckland councillor Cameron Brewer told the Herald he was eyeing selection.
List MP and Education Minister Hekia Parata will not seek re-election either, which creates a fourth ministerial vacancy, but she may keep her portfolio until her likely successor, Nikki Kaye, has returned to work from cancer treatment.
Younger ministers Amy Adams, Jonathan Coleman and Simon Bridges are expected to get big promotions in the reshuffle and be admitted to the "kitchen Cabinet," the informal group of senior ministers who advise the Prime Minister.
There is no suggestion Nick Smith will be sacked, although Building and Housing could go to a new minister.
Guaranteed fresh faces
The National-held seats guaranteed a new MP at next year's general election are:
• Pakuranga, currently held by Maurice Williamson, who will become New Zealand Consul General in Los Angeles;
• Whanganui, held by Chester Borrows;
• East Coast Bays, held by Foreign Affairs Minister Murray McCully, who has announced he won't seek an electorate seat but is yet to announce any retirement plans;
• Helensville, held by former Prime Minister John Key;
• Maungakiekie, held by Local Government Minister Sam Lotu-Iiga;
• Tukituki, held by Small Business Minister Craig Foss.