The 65-year-old thinks that the Amsterdam ArenA would be a good place for the defender to flourish, but it is believed he may turn down a move away from Camp Nou
The Eredivisie champions are in the market for a new defender after selling club captain Jan Vertonghen to Tottenham earlier in the week.
AZ's Niklas Moisander was understood to be Ajax's priority to reinforce their back line, but the Amsterdam club were reportedly priced out of a move for the Finnish stopper.
Ajax sporting director Marc Overmars admitted on Thursday that his side were keeping tabs on Muniesa, and it is now being reported that it was Cruyff who recommended the 20-year-old to the club.
However, Muniesa may not be interested in a move away from Camp Nou as he will have the chance to fight for a place in Barca's squad during the pre-season, with Carles Puyol currently recovering from an injury and Jordi Alba expected to play at the Olympic Games.