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The striker returned from injury towards the end of the season but was no longer able to command a regular place in the team.
"The club must do its homework and so must I. It's a new situation," he told reporters.
"I'm going to calmly sit down and consider everything.
"I still have ambitions of playing every week. I feel fit and I think I can still go on for several years. Take note of my words," said the 31-year-old, who moved to Old Trafford from Arsenal in 2012.
Van Persie said he should have had six or seven more goals than the tally of 10 he netted for the club last season.
"People don't accept that I just scored 10. Actually that's a compliment because they expect more of me on the basis of what I can do. I was the club's second highest goal scorer together with Juan Mata and behind Wayne Rooney (14 goals).
"It's not good that a top club like Manchester United does not have a scorer with 20 or more goals behind his name each season and that is why we only finished fourth."
Van Persie struggled with an ankle injury through the season, blaming a hectic pre-World Cup training programme, as he battled to get fit for Brazil, and then a lack of a break after the tournament last summer.
"After I came back from injury I realised that I would not automatically get back in the starting line-up," he said. "But I didn't have a problem with that because they were playing well at the time.
"These things happen. We are living in an adult world. Louis van Gaal is not the coach of Robin van Persie but of Manchester United with 25 in the squad."
"I have to think in a realistic way, he continued. "It’s my ambition to play the next years. I’m thinking about my family and my children with every decision I take.
"These are very important for me. I’m a real family guy. I think it’s fantastic to see how happy my children and wife are. That’s something I take into consideration when I’m thinking about my future.”
The Dutch captain has made 104 appearances for Manchester United scoring 58 goals in 3 seasons.
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