Musharraf, who himself had a five-year extension as army chief, cautioned that a change in the military leadership at this critical juncture for Pakistan could lead to problems and "everything would go to waste."
"What he is doing right now, it needs continuity and if there is any change in the leadership amidst this all, all good work which has been done so far would go waste," the 72-year-old told Samaa TV last night.
"So I can only wish and suggest that he should stay there," he said.
Gen Sharif, who took over as army chief in 2013, is due to retire in November next year.
Also Read
Media reports have suggested that the army chief is also behind the current drive against corruption in the country.
Pakistani Rangers, which is controlled by the army, has made several high-profile arrests including that of former petroleum minister Asim Hussain in Sindh in recent months as part on an anti-corruption crackdown.
The army claims to have killed more than 3,500 militants in the operation which has now entered its final phase.