Giggs has been appointed as interim boss following the sacking of David Moyes 10 months into his reign as Sir Alex Ferguson's successor, and United beat Norwich City 4-0 in his first game in charge on Saturday.
Nevertheless, outgoing Netherlands manager Louis van Gaal remains the hot favourite to take the Old Trafford vacancy in the summer, and, while admitting that the 62-year-old appears to be in the driving seat, Neville stressed that nothing is confirmed yet while lending his support to Giggs.
"He's an experienced hand. He's won trophies in different countries and managed the biggest clubs in Europe," he told Sky Sports News. "He's the favourite at the moment and we know nowadays, just through the weight of media speculation, sometimes, where jobs are going to go. I think at the moment it's pushing towards him.
"I would have liked to have seen Ryan have two or three games. He started well on Saturday, so let him have two or three more games to see whether he settles into the position and whether he can bed in and be given that role. I don't think there's any certainty wherever you go. There's the idea that Ryan hasn't got experience but he knows the club and there's the idea that Van Gaal has massive experience, but doesn't know the Premier League.
"At the end of the day the owners will do what they want to do. I suppose in some ways they want an experienced hand, but I personally would like to see a British manager be appointed because Manchester United have always appointed British managers. We'll wait and see."
United have never had a manager born outside of the United Kingdom.