Sir Lindsay said the North West's has been "hit hard" by the Covid-19 and is against any vaccines being deployed elsewhere in the country.
It comes just days after a Lancashire health chief confirmed that the North West's Covid-19 vaccine supply is set to be reduced following a report by the Health Service Journal (HSJ) on Tuesday (January 26).
The report said that "the supply of Covid vaccines to the North West region is set to be cut by around a third in February, seemingly due to national shortages and the need for other regions to catch up with vaccinating their priority groups."
The NHS confirmed the weekly supply will be reduced to 200,000 by the second week of the month for Greater Manchester, Lancashire, Cheshire, Merseyside and South Cumbria.
Sir Lindsay took to Twitter and said he has spoken to Matt Hancock, the Health Secretary, and Nadhim Zahawi, who is the minister in charge of the vaccine rollout.
He said: "I have raised this with both the Secretary of State for Health and the Minister for Vaccine Deployment and argued against any reduction as the North West’s health inequalities and high levels of poverty have seen us hit hard by Covid-19 and resulted in us being locked down much longer than others."
Jane Scattergood, Covid-19 vaccination director for NHS Lancashire, confirmed on Wednesday (January 27) that the HSJ report was correct.
She assured the public everyone in the Joint Committee on Vaccination and Immunisation's top four priority categories would still receive their first vaccine, despite reduced numbers.
Ms Scattergood said: "We will complete the top four JCVI priorities by mid-February, even on the reduced vaccine supply.
"We're looking to national NHS leaders and central Government to continue to work hard to increase the supply."