Stephen Thompson, whose 92-year-old mother has been isolating for almost a year, said he was getting worried that she would miss out on the Covid-19 mass vaccination campaign and put her life at risk.
He said: "She has been isolating since March (last year) but has carers (going) in every day, that is the worrying bit."
A woman also raised her concern, saying that her father, who is in his 80s, has not "heard a thing" from the GP.
"Rang (the) GP and they said they ran out of vaccine and don't know when getting more!” she said.
The NHS is currently offering the vaccine to people from the most at risk group, including the healthcare workers and those over 80.
Since the vaccination rollout took off in December, there are at least 15 Covid community vaccination centres set up and running in Sheffield delivering thousands of potentially life-saving jabs.
But those who are eligible for the vaccines will be contacted directly by the NHS when it is their turn to receive it.
For most, this will be in the form of a letter from either their GP or the national booking system.
Clinical Director of Primary Care Network in Sheffield Dr Ollie Hart said it would help if the contact numbers are updated on their GP system to avoid any possible delay.
The NHS has been contacted for comments but has yet to respond.