The striker struggled with injuries throughout the Premier League campaign - but he is confident he is now nearing full fitness.
"After all the physical niggles I had this season it is not obvious that I am going to be at the top of my form," said van Persie.
"I must take it gradually (getting back to full fitness) but I am optimistic, I think, that I will be ready for the beginning of the tournament.
"It is both tiring physically as well as psychologically because each time I thought I was getting back to being fully fit, I had a reverse.
"The coach has confidence in me, which is very pleasing and reassuring."
Van Persie is unlikely to be risked for this Saturday's warm-up match with Ukraine on Saturday.
Dutch coach van Basten added: "I do not want to take a risk with Robin.
"My wish is that he will be 100 per cent fit on June 9 (when Holland open their campaign against Italy)."