The Dutchman has been linked with a move away from Old Trafford following a disappointing campaign that has been hampered by injury.
United boss Louis van Gaal is reportedly tracking a number of strikers in a bid to shake up his attacking options in the summer but former Red Devil Neville reckons Van Persie, 31, will survive the chop.
"No, I wouldn't expect him to leave. United need top quality centre-forwards and I think he will stay," Neville told The Sun.
Reports have linked United with a host of big-money signings suggesting Van Gaal is looking for another extensive summer rebuild.
But Neville reckons the transfer window will be a tame affair this time around with just three new players needed.