PSG are looking to replace Zlatan Ibrahimovic when he leaves at the end of his contract this month, while United are expected to boost their squad after appointing Jose Mourinho as manager following a disappointing 2015/16 Premier League campaign.
Neymar has scored 85 goals in 141 games across all competitions for Barca since joining from Santos in 2013, and Busquets feels the 24-year-old would want to continue playing for the Catalan giants.
“I'm not worried; in the world of football what is meant to happen, happens,” Busquets told Onda Cero. “He has already said he is fine, he is comfortable and I believe he will stay despite the rumours.”
The Spain international also shared his thoughts on Dani Alves and Marc Bartra, who left the La Liga champions at the end of last season.
“They have decided to leave and as a teammate it’s bad news, but you have to respect their decisions,” Busquets added.
“We hope the technical secretary’s call [on replacements] is the best one and we can continue to fight for titles. We have great players at Barca and we will continue to keep fighting at the top for everything.”