Health boards have been asked to look into co-administering the jabs, which the deputy chief medical officer for vaccines said would be "quite a feat".
Flu jabs are often given in GP surgeries while Covid jabs have mostly been given in mass vaccination centres.
Dr Gill Richardson said a number of the large jab centres would close but some smaller sites may be kept open.
The Welsh government's plan is for the Covid rollout to become part of an existing immunisation programme.
It includes moving away from an emergency response to the pandemic and looking at how to deliver the Covid booster like other seasonal jabs.
Dr Richardson said delivering both jabs at the same time could reduce pressure on primary care settings, such as GP surgeries.
"We know that you can give the flu vaccine and Covid vaccine at the same time in different arms," she said.
"We know the early flu strains as they emerge in the east, those viruses are examined and the flu vaccine is affected so a new flu vaccine is developed every year.
"Depending on the timing of that being available, I think there could well be co-administration for many people and that would be an ideal."
* There are about 350,000 people in Wales who qualify for a second booster jab, out of those aged over 75, in care homes or severely immunosuppressed
* Nearly 6.8 million vaccine doses have been given out since the programme started in December 2020
* Wales has reached nearly 80% of its total population with a first dose and 75.2% with a second dose - just behind Scotland in reaching the most of its population.
* For boosters/third doses, both Wales and Scotland have reached 87% of those eligible. That's 61.7% of the total population. Globally, that places Wales sixth among nations of more than a million at reaching the highest proportion of population
* The programme, as it stands, has slowed down considerably since a burst of booster vaccinations in the three weeks before Christmas
* Boosters are now averaging about 1,500 a day, compared with 50,000 at the peak
* Just over 16,200 vaccines were given out in the last week
Throughout the pandemic, leisure centres and a former children's toy shop were transformed into mass vaccination centres to help deliver the vaccine to as many people as possible.
But many of these will close soon with some smaller ones retained by health boards as a precaution.
The spring roll-out of a fourth dose of the Covid jab will be for people aged 75 and over, care home residents and those aged over 12 who are immuno-suppressed.
A further booster is likely to be offered to these groups during the autumn.
The British Medical Association (BMA) in Wales welcomed the autumn move, but expressed some concerns over how surgeries will manage to deliver a fourth vaccine to all priority groups during the spring.
Speaking to BBC Radio Wales, Dr Phil White, chairman of the BMA's Welsh GP committee, said:"While GPs expect, and are willing, to play a role in Covid vaccine booster campaigns, we have heard very little detail about Welsh government's April booster plans.
"Later in the year it would appear sensible to give people both their flu jab and a Covid vaccine booster at the same time, as two separate jabs.
"GPs will be seeing many of their most vulnerable patients to give them the flu jab, so this strategy would help keep patients safe while also complimenting the other support GPs provide."
Health Minister Eluned Morgan said the coronavirus vaccines had "saved countless lives and given us the freedom and confidence to restart our lives in the midst of an ongoing global health emergency".
She added: "This strategy sets out our plans for 2022 and beyond, including a commitment to deliver a regular Covid-19 vaccination programme while planning for any potential surge capacity, should we need to, in the case of a new pandemic wave or a new coronavirus variant."