Joe Foster claims providing vaccines in the 13 high-rise blocks, which mainly house pensioners, could work.
The Parkfoot Court resident insists a vaccination model similar to the programme being rolled out across care homes could be used as carers already pay regular visits to the flats.
He said: “The high-rises have a lot of senior citizens and a lot of them have carers who come in twice or four times a day.
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“I would like to think the health people would treat it like a care home and do the vaccinations in the building itself.
“If they can do vaccinations at an old folks’ home, I don’t see why they can’t do a high rise flat.
“I think they should consider the high-rise flats in our area where the vast majority of people are elderly.”
With vaccines already being administered at numerous hubs across the region, NHS Forth Valley says it has plans in place to reach “initial priority groups”.
A spokesperson said: “All NHS boards across Scotland are delivering the Covid-19 vaccine to the initial priority groups at a range of community venues, in line with the Scottish Government’s Covid-19 Vaccine Deployment Plan.
“More than 30 community hubs and local GP practices are delivering the vaccine across Forth Valley, including three community hubs and six local GP practices in the Falkirk area.
“Community nurses are also delivering the vaccine at home to older people who are housebound and unable to travel to a local vaccination clinic.
“In addition, a dedicated immunisation team is delivering the vaccine to care home residents in all 65 care homes across the Forth Valley area.
“If anyone has any difficulties accessing a vaccination session they can contact the Covid-19 helpline for advice.”
Michael Matheson, Falkirk West MSP, feels Falkirk’s high-rises could become a “sensible” solution.
He said: “The suggestion made by the Parkfoot Court resident is perfectly reasonable and worthy of consideration.
“At the same time, I am aware NHS Forth Valley, like all other health boards, is having to manage a very significant logistical challenge in rolling out the vaccine.
“However, if there is scope to expand on the number of community venues used in the coming weeks, the high flats would seem a sensible choice.”
Falkirk South Councillor Pat Reid is less convinced.
He said: “Not all of the facilities have a community room.
“I think the main issue would be having a hygienic facility. It’s worth the health board considering but, with the complications, it’s a bit difficult.”
Councillor Fiona Collie, Integrated Joint Board chairwoman, added: “I understand the views of the residents of the high-rise community and I know people would like to be vaccinated as close to home as possible.
“However, the Covid-19 vaccination programme is a large and complex one and Forth Valley is delivering the vaccine in a number of community hubs and GP practices.
“Arrangements are also being made to vaccinate a number of more vulnerable people at home who are unable to attend a local vaccination clinic.”