The 36-year-old has been sidelined this season after he required a procedure to treat an irregular heart rhythm, but he has been offered a coaching role at United if he decides to call time on his playing career.
"Everyone knows this sort of enthusiastic association that I keep with the clubs, and that is the way I'm doing it".
Galatasaray and Besiktas have been in talks with the midfielder.
Kluivert has scored eight goals in 40 appearances, notably achieving a feat his father his father could not; scoring a quite stunning hat-trick against Roda JC back in November. The squad have one more training session left, on Thursday afternoon, before returning to Manchester on Friday.
"Their philosophy and their style is something to be admired, but that's why it's something we're looking forward to".
Yahoo Sport claimed in December he was one of a number of options being considered by United ahead of the January window, named on a shortlist that also included Monaco's Thomas Lemar, Bordeaux starlet Malcom and Christian Pulisic of Borussia Dortmund.
"But we're a team that's growing and we're performing really well at a high level at the moment".
Manchester United and Manchester City are all set to take their feud out into the transfer market with Jose Mourinho refusing to give-up on what looks like a season lost to his arch-rival Pep Guardiola.
"They had top players out there, and at times, we outplayed them".
Burnley sat sixth in the Premier League, above Arsenal and level on points with fourth-placed Tottenham, prior to their current winless run.