Falcao must earn his place - RVP
United pulled off the most eye-catching transfer of deadline day when they signed the Colombia forward on loan from Monaco for £6million.
Despite the sale of Danny Welbeck to Arsenal, United still have some formidable options in attack, including Van Persie and Wayne Rooney.
For that reason, the Dutch striker believes the club's new Colombian import will need to work hard to earn his place in manager Louis van Gaal's starting XI.
"I welcome his arrival, he makes us better," Van Persie told Fox Sports NL.
"At a top club you should always go for the best, which also fits my philosophy. Falcao must fight for his place, as I also have to. We must duke with Wayne Rooney and James Wilson to see who is playing."
Some speculated United signed Falcao as a replacement for Van Persie, who was rumoured to require knee surgery.
Van Persie dismissed that speculation, adding: "I am impressed that people can pick up the imagination to invent something like that.
"I do not know where it comes from and can say with my hand on my heart that I won't be in a hospital to have the operation."
United, meanwhile, confirmed on Wednesday that their 21-year-old right-back Guillermo Varela has joined Real Madrid on loan until the end of the season.
David Moyes made Varela his first signing as United boss, but the defender is yet to play for the Red Devils and will feature in Madrid's reserve team.