Black Cats sporting director Roberto De Fanti and chief scout Valentino Angeloni are understood to have been in Italy last week and met with Inter Milan director Piero Ausilio, with Bessa, Duncan and Mbaye top of the agenda.
However, 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 and he told Sky Sports that Inter were currently not looking to let the young Senegalese defender leave, and he understood that was the case with all three players Sunderland were looking at.
"Mbaye is not available, at the moment at least," Accardi told Sky Sports.
"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."
Mbaye, 18, is a central defender, whilst 20-year-olds Bessa and Duncan are midfielders, and Inter believe all three players have bright futures with the club.