It would give tenants the legal right to request a pet in their home, which landlords cannot unreasonably refuse.
The change is a part of a wide-range of proposed rental reforms including the abolition of no-fault evictions.
But one landlord's association wants more information on the circumstances in which landlords can refuse pets.
Housing campaigners have described the Renters (Reform) Bill as a "huge opportunity" to improve the lives of the 11 million renters in England.
And for single mother Charity Micheal, the law change would make it easier to find a place to live.
"My daughter and I have viewed over 50 properties, made offers and were constantly rejected either due to the landlord or the leasehold not wanting pets," said Ms Micheal, who works for the NHS.
She told the BBC most landlords will refuse her applications "once they know I am a single mother with only one income or that I am a dog mum".
"This had been very stressful for me as I have lived in my current area for almost two years and have had to move home three times and this will be the fourth."
Student nurse Kayleigh Berry, in Great Yarmouth, has experienced a similar challenge. She has been looking for a property for about four months, and so far, has had just 10 viewings. None of her three applications have been successful.
She said when prospective landlords hear about her pets - three cats and a dog - they become less inclined to proceed with the application process.
"Pets are the main thing. We can't even get viewings half the time. We either don't hear back or it's a no," she told the BBC.
The Battersea Dogs & Cats Home in south London said the reforms will significantly reduce the number of pets taken in by shelters.
"Not only will this bill bring us one step closer to significantly reducing the number of dogs and cats we see being needlessly separated from their owners, it will also open up the many joys of pet ownership to millions of renters in the future," said Michael Webb, head of policy and public affairs.
They said two elderly Chihuahuas, Harvey and Rosco, were taken in after their former owner's landlord sold the property, and the owner was unable to find a pet-friendly rental.
On their website, the charity Dogs Trust say the main reason for pets being handed over is "change in owners' circumstances, such as being unable to live in a rented property with a pet."
Its chief executive Owen Sharp described the reforms as a "potential game changer".
"We're receiving hundreds of calls each week from desperate owners forced to rehome their dogs due to a lack of pet friendly accommodation," he said.
"The measures announced today as part of the Renters (Reform) Bill will mean that many more dogs can stay living with their loving families."
The National Residential Landlords Association (NRLA) said the bill could also allow landlords to request their tenants take out insurance to cover any potential damage caused by the pets.
"We welcome the government's plans...which will enable landlords to ask pet owners to have the required insurance to cover such damage," its policy director Chris Norris, Policy Director said.
He also asked the government provide more information on what constitutes unreasonable grounds to withhold consent.
"It still remains unclear as to the exact grounds on which landlords can refuse to let to tenants with a pet, so the government must provide greater clarity on this point," he said.
Mr Norris encouraged a mutual agreement on having pets in rental properties between landlords and tenants.