It is believed that Inter have told Sunderland that they will have to wait until later in pre-season once new coach Walter Mazzarri has assessed the players.
Mbaye's agent is Beppe Accardi told Sky Sports: "Mbaye is not available, at the moment at least.
"Sunderland want him and perhaps there could be a loan, but the coach wants to see him in pre-season and then assess things.
"I imagine it is the same with Duncan and Bessa, all three are very good players and it is clear to see why Sunderland would want them.
"We will have to see what happens later in the summer."