The Championship leaders are unlikely to want to part with their talented 20-year-old centre-back, but Meulensteen believes he has the qualities to strengthen his Fulham squad.
Moore has 18 months left to run on the three-year deal he signed in September 2012 and has impressed during his 23 league appearances for Leicester this season.
An initial offer for Moore has been tabled by Fulham and Meulensteen is now leaving the matter with the club's chief executive Alistair Mackintosh.
"We've put a bid in, but it's up to Alistair Mackintosh," said Meulensteen on Thursday at his press conference to preview Sunday's FA Cup fourth-round tie at Sheffield United.
"(Reports) are quite accurate, but Macintosh is dealing with transfers.
"I'm focused on training the players."
Fulham sit 17th in the Premier League, one point above the bottom three.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1