Staff from the unit had been moved temporarily to Wythenshawe Hospital in 2021 to tackle increased demand amid a shortage of nurses.
Mr Fisher said the unit’s permanent closure would see the “continued relocation” of staff to Wythenshawe, adding all other services at the Altrincham site would not be affected.
Connor Rand, Labour MP for Altrincham and Sale, said he was “deeply disappointed” at the move.
He said the unit was a service many in his constituency “relied on and appreciated”, adding he would write to the NHS board urging them to reconsider.
Liberal Democrat leader councillor Shaun Ennis, said the loss of urgent care provision in the Altrincham and the South Trafford area was “completely unacceptable”.
He told the Local Democracy Reporting Service it would have a “devastating” impact for those “most in need”, adding it was “lazy and short-sighted” given plans for thousands of new homes in the area.
Conservative leader councillor Nathan Evans said the proposal was the “death knell” of the hospital, adding Labour councillors had refused to back his motion to call for the unit to be reopened.
The review’s authors said NHS guidance was clear that “stand-alone” units should now be commissioned to cut “the often confusing mix of urgent care services”.
Altrincham also had good public transport links and high rates of car ownership, it added.
A final decision on the recommendation is due to be made at an NHS Greater Manchester Integrated Care Board meeting on 18 September.
