The 30-year-old Argentinian is out of contract at the end of the season but Mowbray knows the club's financial situation may mean he will not be able to hang on to the player.
He told Boro's official website: "It's important I say how much I value Julio's talent. He is a fabulous lad and a fantastic football player.
"Discussions about his future are to be had, really. Over the next couple of weeks I will speak to him about what we can do and then he will no doubt go away and consider his options.
"We have to be transparent with Julio so he knows where this football club is going. A player of his ability will have different options, I am sure.
"If his decision is to sign for Middlesbrough again for whatever we are able to put on the table, I will be delighted. But whatever happens, I wish him well."
Source: PA
Source: PA