Since graduating from the club's academy system, Mingueza has established himself as a valuable squad member in the senior setup.
The 23-year-old has made a total of 66 appearances in all competitions, a total of 32 starts and 14 substitute outings coming in La Liga.
However, Barcelona are currently going through a period of transition with a wide range of high-profile names being linked with a switch to Camp Nou.
That has resulted in Mingueza being left surplus to requirements in Xavi's squad, and it is deemed only a matter of time before he makes his exit.
According to Marca, Monza are the favourites to secure a deal for the versatile defender as they bid to establish themselves in Serie A.
I Biancorossi are currently preparing for their first-ever year in Italy's top flight, and several high-profile players have already been signed.
Monza now hope to fend off any rival interest to secure the signature of Mingueza, who is capable of playing in the middle or right-hand side of the defence.
With Mingueza having just a year remaining on his contract, Barcelona are ready to do business for between €5m (£4.3m) and €8m (£6.9m).
Girona had also been interested in signing Mingueza after earning a return to La Liga, but it is reported that the newcomers cannot afford to meet Barcelona's valuation.
Parting ways with several of their squad members is necessary for Barcelona if they are to follow the additions of Christensen and midfielder Franck Kessie.
Club officials are also waiting to see if winger Ousmane Dembele will accept the contract offer which has been on the table for several weeks, the Frenchman having become a free agent on July 1. body check tags ::