Simba and Willow came into the care of Cats Protection's Milton Keynes branch at the beginning of the year.
The female tabby and black and white male are so devoted to each other that they cannot be separated.
Both are five years old and Cats Protection say they were much loved in their previous home.
"But sadly they became very stressed after the arrival of a baby,” said a spokesman.
The pair are currently being cared for by one of the charity’s fosterers and so far nobody has shown an interest in adopting them.
To make it even more difficult, black and white Willow has a heart murmur and needs a yearly heart scan to monitor his progress. But this will be funded by Cats Protection, and he does not need medication
A charity spokesman said: “Willow has the softest coat and a soft, soppy nature. He loves being at the top of their cat tree, and often, if he sees you coming, he’ll leap to the top and start rolling and purring ready for a gentle tummy rub.”
She added: “Simba is a very chatty cat and likes to have long conversations with her fosterers, she loves a good game of fetch with her little soft ball, most times dropping it back near your feet.
"They love to play together, and will ambush each other and then tear around the house, providing their fosterers with lots of laughs.”
The pair need to be rehomed together in a home with no children or likelihood of children in the future, and no other pets.
They are mostly indoor cats, but do like access to a garden, especially in good weather when they enjoy being in the sun. They are happy using a cat flap.
If you can offer Willow and Simba a home or any of the other cats in the Branch’s care, please call Cats Protection 01908 984799.
The branch is run entirely by unpaid volunteers who the work around their own busy lives, jobs and family commitments.
In 2021, despite the impact of the COVID-19 pandemic, they rehomed more than 220 stray and unwanted cats and kittens.