The 35-year-old defender, who has played for United for 18 years, comes to the end of his contract in June and has yet to be offered a new deal.
"I don't know. I'm not thinking about it," he said when asked about extending his career beyond this season.
"I'm at the age now where I just want to stay fit and concentrate on the last few days of the season."
Neville is part of a famed generation at Old Trafford under manager Sir Alex Ferguson, that rose through the ranks with the likes of David Beckham, Nicky Butt, Paul Scholes, Ryan Giggs and his brother Phil to form part of the group known as "Fergie's fledglings".
588 appearances for Man UtdWon 3 FA cups with Man UtdWon 8 Premier League titles Won 2 Champions League titles 85 caps for England, more than any other right-back
But the former United skipper has struggled to make the team recently, falling behind Wes Brown and Rafael da Silva in Ferguson's selection for right-back.
The veteran defender added: "The difference now is that when I play games I get fitter, but when I get injured it takes me a month to get back."
Neville has been plagued by repeated injuries since breaking his ankle in a match against Bolton in 2007.
In the last three season he has suffered repeated muscular injuries resulting in only a sporadic presence on the field.
He has been increasingly sidelined as he has aged, missing out on both the 2008 and 2009 Champions League finals.
Despite such worries, Neville came on as a substitute in the Carling Cup final on Sunday for around 25 minutes as United battled to retain the league cup, beating Aston Villa 2-1.
Source: BBC Sport
Source: BBC Sport