Ibrahimovic joined the Premier League giants in the summer after his contract with PSG came to an end.
United are hot favourites to win this year's Europa League and Zlatan Ibrahimovic wants his side to live up to their expectations to maintain excitement for the rest of the season.
United manager Jose Mourinho is said to be expecting the huge Swede to stay with his squad next season.
When asked by Omnisport whether Ibrahimovic was worthy of an extended deal despite his veteran status, Neville said: "I'd say yes".
"I think United needed personalities and characters after what happened in the previous few seasons". The striker played a key role in Thursday's hard-fought win over FC Rostov, his flick setting up Juan Mata to score the only goal of the game and send United through to the quarter-finals. "The reality is, I'm not quite sure that will be able to happen as he continues to get a little bit older".
He has scored 26 goals this season and is showing no signs of slowing down despite his advancing years.
Ibrahimovic also commented on how hard United found it to beat their Russian opponents at Old Trafford.
But with Ibrahimovic set to serve the final two matches of a three-game ban against Middlesbrough and West Brom in the Premier League for elbowing Bournemouth's Tyrone Mings, Neville believes it is a flawless opportunity for Rashford to prove his quality, having impressed in the 1-0 FA Cup quarter-final loss at Chelsea.
The former Barcelona forward added, "My family was very happy in Milan", talking about his move to another Italian club, AC Milan.