Barry Rackham, 60, and teenage son Andrew had expected to get the keys to their new rented home in Prospecthill Court, Greenock, in time for moving out of their own property in West Woodside Avenue on Wednesday.
However, they say they were told on Monday by River Clyde Homes that their new home will now not be ready for at least another month, as it needs a new kitchen.
Barry's other son, Greg, is now trying to sort out the problem.
Greg said: "My dad was offered the house at Prospecthill Court and was told it would be ready by the time he sold his own.
"But now we are being told it will be over a month, so he will be homeless.
"It is quite distressing and my dad is quite stressed.
"I have no idea what he and Andrew will do."
Greg, 35, lives in Greenock with his own young family and is only able to put his dad and brother up for a few days.
He told the Tele: "We will try and put them up for a few days but we don't have room for all their stuff.
"River Clyde Homes have referred my dad to the homeless centre and I am quite shocked, actually.
"They want £200 a week each for them to stay there, because my dad works nightshift in Tesco as a shelf-stacker."
River Clyde Homes bosses say they are are hopeful that the Prospecthill Court home will soon be ready for the Rackhams to move in.
A spokesman said: "The property was viewed with a void property officer and accepted by Mr Rackham.
"The officer advised that the void works required to bring the property to a lettable standard had not yet begun, and based on the large volume of void properties being worked on, could not guarantee an exact date for when the property would be ready.
"Works are now under way at the property and it is hoped that these works will be completed in the coming weeks to allow Mr Rackham to take up his tenancy."